TSTP Solution File: LAT195-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT195-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 06:26:03 EDT 2022
% Result : Unsatisfiable 2.74s 3.01s
% Output : Refutation 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT195-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 30 07:02:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.74/3.00 ============================== Prover9 ===============================
% 2.74/3.00 Prover9 (32) version 2009-11A, November 2009.
% 2.74/3.00 Process 11781 was started by sandbox on n008.cluster.edu,
% 2.74/3.00 Thu Jun 30 07:02:23 2022
% 2.74/3.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11628_n008.cluster.edu".
% 2.74/3.00 ============================== end of head ===========================
% 2.74/3.00
% 2.74/3.00 ============================== INPUT =================================
% 2.74/3.00
% 2.74/3.00 % Reading from file /tmp/Prover9_11628_n008.cluster.edu
% 2.74/3.00
% 2.74/3.00 set(prolog_style_variables).
% 2.74/3.00 set(auto2).
% 2.74/3.00 % set(auto2) -> set(auto).
% 2.74/3.00 % set(auto) -> set(auto_inference).
% 2.74/3.00 % set(auto) -> set(auto_setup).
% 2.74/3.00 % set(auto_setup) -> set(predicate_elim).
% 2.74/3.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.74/3.00 % set(auto) -> set(auto_limits).
% 2.74/3.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.74/3.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.74/3.00 % set(auto) -> set(auto_denials).
% 2.74/3.00 % set(auto) -> set(auto_process).
% 2.74/3.00 % set(auto2) -> assign(new_constants, 1).
% 2.74/3.00 % set(auto2) -> assign(fold_denial_max, 3).
% 2.74/3.00 % set(auto2) -> assign(max_weight, "200.000").
% 2.74/3.00 % set(auto2) -> assign(max_hours, 1).
% 2.74/3.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.74/3.00 % set(auto2) -> assign(max_seconds, 0).
% 2.74/3.00 % set(auto2) -> assign(max_minutes, 5).
% 2.74/3.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.74/3.00 % set(auto2) -> set(sort_initial_sos).
% 2.74/3.00 % set(auto2) -> assign(sos_limit, -1).
% 2.74/3.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.74/3.00 % set(auto2) -> assign(max_megs, 400).
% 2.74/3.00 % set(auto2) -> assign(stats, some).
% 2.74/3.00 % set(auto2) -> clear(echo_input).
% 2.74/3.00 % set(auto2) -> set(quiet).
% 2.74/3.00 % set(auto2) -> clear(print_initial_clauses).
% 2.74/3.00 % set(auto2) -> clear(print_given).
% 2.74/3.00 assign(lrs_ticks,-1).
% 2.74/3.00 assign(sos_limit,10000).
% 2.74/3.00 assign(order,kbo).
% 2.74/3.00 set(lex_order_vars).
% 2.74/3.00 clear(print_given).
% 2.74/3.00
% 2.74/3.00 % formulas(sos). % not echoed (13 formulas)
% 2.74/3.00
% 2.74/3.00 ============================== end of input ==========================
% 2.74/3.00
% 2.74/3.00 % From the command line: assign(max_seconds, 300).
% 2.74/3.00
% 2.74/3.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.74/3.01
% 2.74/3.01 % Formulas that are not ordinary clauses:
% 2.74/3.01
% 2.74/3.01 ============================== end of process non-clausal formulas ===
% 2.74/3.01
% 2.74/3.01 ============================== PROCESS INITIAL CLAUSES ===============
% 2.74/3.01
% 2.74/3.01 ============================== PREDICATE ELIMINATION =================
% 2.74/3.01
% 2.74/3.01 ============================== end predicate elimination =============
% 2.74/3.01
% 2.74/3.01 Auto_denials:
% 2.74/3.01 % copying label prove_distributivity to answer in negative clause
% 2.74/3.01
% 2.74/3.01 Term ordering decisions:
% 2.74/3.01
% 2.74/3.01 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 2.74/3.01 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 2.74/3.01
% 2.74/3.01 ============================== end of process initial clauses ========
% 2.74/3.01
% 2.74/3.01 ============================== CLAUSES FOR SEARCH ====================
% 2.74/3.01
% 2.74/3.01 ============================== end of clauses for search =============
% 2.74/3.01
% 2.74/3.01 ============================== SEARCH ================================
% 2.74/3.01
% 2.74/3.01 % Starting search at 0.01 seconds.
% 2.74/3.01
% 2.74/3.01 ============================== PROOF =================================
% 2.74/3.01 % SZS status Unsatisfiable
% 2.74/3.01 % SZS output start Refutation
% 2.74/3.01
% 2.74/3.01 % Proof 1 at 2.00 (+ 0.04) seconds: prove_distributivity.
% 2.74/3.01 % Length of proof is 145.
% 2.74/3.01 % Level of proof is 39.
% 2.74/3.01 % Maximum clause weight is 43.000.
% 2.74/3.01 % Given clauses 357.
% 2.74/3.01
% 2.74/3.01 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 2.74/3.01 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 2.74/3.01 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 2.74/3.01 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 2.74/3.01 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 2.74/3.01 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 2.74/3.01 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 2.74/3.01 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 2.74/3.01 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 2.74/3.01 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 2.74/3.01 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 2.74/3.01 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 2.74/3.01 13 meet(A,join(B,meet(C,D))) = meet(A,join(B,meet(C,join(B,meet(D,join(B,C)))))) # label(equation_H34) # label(axiom). [assumption].
% 2.74/3.01 14 meet(A,join(B,meet(C,join(B,meet(D,join(B,C)))))) = meet(A,join(B,meet(C,D))). [copy(13),flip(a)].
% 2.74/3.01 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 2.74/3.01 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 2.74/3.01 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 2.74/3.01 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 2.74/3.01 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 2.74/3.01 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)])].
% 2.74/3.01 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 2.74/3.01 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 2.74/3.01 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)])].
% 2.74/3.01 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 2.74/3.01 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 2.74/3.01 26 join(A,meet(B,join(A,meet(C,join(A,B))))) = join(A,meet(B,C)). [para(14(a,1),1(a,1)),rewrite([7(8),14(8),1(5)]),flip(a)].
% 2.74/3.01 34 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 2.74/3.01 35 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 2.74/3.01 36 one != A | complement(A) = zero. [back_rewrite(34),rewrite([35(2)]),xx(a)].
% 2.74/3.01 37 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([35(5)])].
% 2.74/3.01 39 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(22(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),10(6),7(5),10(6,R),7(5)])].
% 2.74/3.01 40 complement(join(A,one)) = zero. [hyper(36,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 2.74/3.01 42 join(A,one) = one. [para(40(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 2.74/3.01 43 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([42(5)])].
% 2.74/3.01 58 join(A,meet(complement(A),join(A,B))) = join(A,meet(B,complement(A))). [para(3(a,1),26(a,1,2,2,2,2)),rewrite([18(3),7(6)])].
% 2.74/3.01 59 join(A,meet(B,join(A,meet(C,join(B,A))))) = join(A,meet(B,C)). [para(26(a,1),8(a,2)),rewrite([8(1),8(5)])].
% 2.74/3.01 60 join(A,join(B,meet(C,join(A,meet(D,join(A,C)))))) = join(A,join(B,meet(C,D))). [para(26(a,1),12(a,2,2)),rewrite([8(5),12(9,R),8(8)])].
% 2.74/3.01 61 meet(A,B) != zero | join(A,meet(B,C)) != one | meet(B,join(A,meet(C,join(A,B)))) = complement(A). [para(26(a,1),17(b,1)),rewrite([22(5)]),flip(c)].
% 2.74/3.01 62 join(A,meet(one,join(A,B))) = join(A,B). [para(42(a,1),26(a,1,2,2,2,2)),rewrite([18(3),7(6),18(6)])].
% 2.74/3.01 63 join(A,meet(join(A,B),join(A,meet(C,join(A,B))))) = join(A,meet(C,join(A,B))). [para(23(a,1),26(a,1,2,2,2,2)),rewrite([7(8)])].
% 2.74/3.01 64 join(A,meet(join(B,complement(A)),join(A,C))) = join(A,meet(C,join(B,complement(A)))). [para(43(a,1),26(a,1,2,2,2,2)),rewrite([18(4),7(8)])].
% 2.74/3.01 65 join(A,meet(join(B,meet(A,C)),join(A,meet(D,join(A,B))))) = join(A,meet(D,join(B,meet(A,C)))). [para(25(a,1),26(a,1,2,2,2,2)),rewrite([7(10)])].
% 2.74/3.01 69 join(A,meet(meet(B,join(A,C)),join(A,meet(B,C)))) = join(A,meet(B,meet(C,join(A,C)))). [para(26(a,1),26(a,1,2,2)),rewrite([7(3),7(9),10(9,R),7(8)])].
% 2.74/3.01 70 join(A,join(B,meet(one,join(A,C)))) = join(A,join(C,B)). [para(62(a,1),12(a,2,2)),rewrite([8(4),12(7),8(6),12(7,R),8(6)])].
% 2.74/3.01 72 join(A,meet(meet(one,join(A,B)),join(A,meet(C,join(A,B))))) = join(A,meet(C,meet(one,join(A,B)))). [para(62(a,1),26(a,1,2,2,2,2)),rewrite([7(12)])].
% 2.74/3.01 73 join(A,meet(B,join(A,B))) = join(A,B). [para(62(a,1),26(a,1,2,2)),rewrite([18(5)])].
% 2.74/3.01 75 meet(A,B) != zero | join(A,B) != one | meet(B,join(A,B)) = complement(A). [para(73(a,1),17(b,1)),rewrite([22(3)]),flip(c)].
% 2.74/3.01 76 join(A,meet(one,join(B,complement(A)))) = one. [para(43(a,1),73(a,1,2,2)),rewrite([7(4),43(8)])].
% 2.74/3.01 77 join(A,meet(join(A,B),join(B,meet(A,C)))) = join(A,B). [para(25(a,1),73(a,1,2,2)),rewrite([7(4),25(8)])].
% 2.74/3.01 82 join(A,meet(one,complement(A))) = one. [para(2(a,1),76(a,1,2,2))].
% 2.74/3.01 86 meet(one,complement(A)) = complement(A). [hyper(17,a,37,a,b,82,a),flip(a)].
% 2.74/3.01 90 join(one,complement(A)) = one. [para(86(a,1),6(a,1,2))].
% 2.74/3.01 94 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),39(a,2)),rewrite([8(3),10(6,R),7(5),10(5,R),7(4)])].
% 2.74/3.01 95 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(39(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),10(3,R),7(2),10(8,R),7(7),10(7),7(6),10(7,R),7(6)])].
% 2.74/3.01 143 join(A,meet(zero,complement(A))) = A. [para(19(a,1),58(a,1,2,2)),rewrite([7(2),4(2),19(2)]),flip(a)].
% 2.74/3.01 146 join(A,meet(complement(A),join(B,meet(A,C)))) = join(A,meet(B,complement(A))). [para(25(a,1),58(a,1,2,2)),rewrite([58(4),7(7)]),flip(a)].
% 2.74/3.01 151 join(A,meet(B,meet(complement(A),join(A,meet(C,join(A,B)))))) = join(A,meet(meet(B,C),complement(A))). [para(26(a,1),58(a,1,2,2)),rewrite([58(5),7(10),10(10,R),7(9)]),flip(a)].
% 2.74/3.01 166 join(A,join(B,meet(zero,complement(A)))) = join(A,B). [para(143(a,1),12(a,2,2)),rewrite([8(4),8(6)])].
% 2.74/3.01 184 join(A,join(meet(zero,complement(A)),meet(B,C))) = join(A,meet(B,C)). [para(26(a,1),166(a,2)),rewrite([8(8),60(9)])].
% 2.74/3.01 194 join(join(A,B),meet(A,join(join(A,B),meet(C,join(A,B))))) = join(join(A,B),meet(A,C)). [para(23(a,1),59(a,1,2,2,2,2))].
% 2.74/3.01 199 join(meet(A,join(B,meet(C,join(A,B)))),meet(B,join(meet(A,join(B,meet(C,join(A,B)))),meet(D,join(B,meet(A,C)))))) = join(meet(A,join(B,meet(C,join(A,B)))),meet(B,D)). [para(26(a,1),59(a,1,2,2,2,2)),rewrite([8(1),8(5),8(15)])].
% 2.74/3.01 202 join(complement(A),meet(one,join(B,complement(A)))) = join(B,complement(A)). [para(90(a,1),59(a,1,2,2,2,2)),rewrite([18(5),8(4),7(9),18(9),8(8)])].
% 2.74/3.01 315 meet(complement(A),join(B,complement(A))) = complement(A). [para(202(a,1),5(a,1,2))].
% 2.74/3.01 330 join(A,meet(complement(A),meet(join(A,B),join(A,meet(C,join(A,B)))))) = join(A,meet(C,meet(complement(A),join(A,B)))). [para(63(a,1),58(a,1,2,2)),rewrite([58(6),7(4),10(4,R),7(3),7(12)]),flip(a)].
% 2.74/3.01 355 join(A,meet(join(B,complement(A)),join(C,complement(A)))) = one. [para(43(a,1),64(a,1,2,2)),rewrite([7(4),76(5)]),flip(a)].
% 2.74/3.01 428 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(6(a,1),65(a,1,2,2,2,2)),rewrite([7(4),6(5),7(4),6(5)]),flip(a)].
% 2.74/3.01 432 join(A,meet(B,join(zero,meet(A,C)))) = A. [para(19(a,1),65(a,1,2,2,2,2)),rewrite([7(4),6(5),7(4),6(5)]),flip(a)].
% 2.74/3.01 444 join(A,meet(one,join(B,meet(A,C)))) = join(A,B). [para(62(a,1),65(a,1,2,2)),rewrite([7(4),77(5)]),flip(a)].
% 2.74/3.01 477 join(complement(A),meet(B,complement(A))) = complement(A). [para(202(a,1),65(a,1,2,2)),rewrite([7(4),2(8),7(7),5(7),2(3),7(6),62(9)]),flip(a)].
% 2.74/3.01 512 join(complement(A),meet(B,join(zero,complement(A)))) = complement(A). [para(315(a,1),432(a,1,2,2,2))].
% 2.74/3.01 595 join(zero,complement(A)) = complement(A). [para(512(a,1),202(a,1)),flip(a)].
% 2.74/3.01 596 meet(zero,complement(A)) = zero. [para(595(a,1),5(a,1,2))].
% 2.74/3.01 599 join(A,join(zero,meet(B,C))) = join(A,meet(B,C)). [back_rewrite(184),rewrite([596(3)])].
% 2.74/3.01 682 join(complement(A),meet(one,join(A,meet(B,complement(A))))) = one. [para(58(a,1),444(a,1,2,2)),rewrite([8(9),3(9)])].
% 2.74/3.01 704 join(zero,meet(A,B)) = meet(A,B). [para(599(a,1),2(a,1)),rewrite([8(5),599(5),2(3)]),flip(a)].
% 2.74/3.01 959 join(A,meet(B,meet(one,join(A,C)))) = join(A,meet(B,join(A,C))). [para(10(a,1),72(a,2,2)),rewrite([72(8),18(8),7(7)])].
% 2.74/3.01 962 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(72(a,1),25(a,1,2)),rewrite([959(8),12(7,R),70(7),8(8),62(8)])].
% 2.74/3.01 991 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(962(a,1),12(a,1)),rewrite([8(5)]),flip(a)].
% 2.74/3.01 1026 join(join(A,B),meet(A,C)) = join(A,B). [back_rewrite(194),rewrite([991(5),5(3),8(2),23(2)]),flip(a)].
% 2.74/3.01 1041 join(complement(join(A,B)),meet(one,join(A,B))) = one. [para(1026(a,1),682(a,1,2,2))].
% 2.74/3.01 1070 meet(one,join(A,B)) = complement(complement(join(A,B))). [para(1041(a,1),17(b,1)),rewrite([10(6),7(5),86(5),4(4)]),flip(c),xx(a),xx(b)].
% 2.74/3.01 1082 join(A,join(B,complement(join(A,B)))) = one. [para(1041(a,1),60(a,1,2)),rewrite([42(2),42(3),18(3),7(5),18(5),8(4)]),flip(a)].
% 2.74/3.01 1347 join(A,meet(complement(A),join(B,complement(join(A,B))))) = one. [para(1082(a,1),58(a,1,2,2)),rewrite([18(3),3(2),7(6)]),flip(a)].
% 2.74/3.01 1421 complement(complement(A)) = A. [para(2(a,1),1070(a,1,2)),rewrite([7(2),18(2),2(1)]),flip(a)].
% 2.74/3.01 1449 meet(one,join(A,B)) = join(A,B). [back_rewrite(1070),rewrite([1421(6)])].
% 2.74/3.01 1472 join(complement(A),meet(join(A,B),join(A,C))) = one. [para(1421(a,1),355(a,1,2,1,2)),rewrite([8(2),1421(4),8(3)])].
% 2.74/3.01 1795 join(complement(A),meet(A,join(B,complement(join(B,complement(A)))))) = one. [para(1421(a,1),1347(a,1,2,1)),rewrite([8(3)])].
% 2.74/3.01 1847 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(94(a,1),10(a,1)),rewrite([7(7),20(7)]),flip(a)].
% 2.74/3.01 1862 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(94(a,1),69(a,1,2,2,2)),rewrite([1847(4),10(2,R),1(1),7(6),10(6,R),1(5),1847(8),10(6,R),1(5),1847(9),10(7,R),1(6),1847(8),20(6)])].
% 2.74/3.01 1906 meet(meet(A,B),join(A,C)) = meet(A,B). [para(1026(a,1),1847(a,1,2))].
% 2.74/3.01 1933 join(A,meet(meet(A,B),join(C,meet(A,D)))) = A. [para(1906(a,1),65(a,1,2,2,2)),rewrite([6(4),7(3),6(4)]),flip(a)].
% 2.74/3.01 1963 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(1026(a,1),95(a,1,2,2,2,2)),rewrite([10(6,R),7(5),10(5,R),7(4),10(4,R),1(3),10(8,R)]),flip(a)].
% 2.74/3.01 2060 join(A,meet(meet(A,B),complement(C))) = A. [para(477(a,1),1933(a,1,2,2))].
% 2.74/3.01 2068 join(A,meet(meet(A,B),join(C,D))) = A. [para(991(a,1),1933(a,1,2,2))].
% 2.74/3.01 2069 meet(meet(A,B),join(C,meet(A,D))) = meet(A,meet(B,join(C,meet(A,D)))). [para(1933(a,1),1847(a,1,2)),rewrite([7(5),1963(5),20(5)]),flip(a)].
% 2.74/3.01 2094 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(1847),rewrite([2069(4)])].
% 2.74/3.01 2163 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(2060(a,1),2094(a,1,2,2)),rewrite([7(3),10(4,R),10(3),7(2),10(3,R),7(2),20(4)]),flip(a)].
% 2.74/3.01 2164 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(2068(a,1),2094(a,1,2,2)),rewrite([7(3),10(4,R),10(3),7(2),10(3,R),7(2),20(4)]),flip(a)].
% 2.74/3.01 2167 join(A,meet(B,meet(complement(A),join(A,meet(C,join(A,B)))))) = join(A,meet(B,meet(C,complement(A)))). [back_rewrite(151),rewrite([2163(10)])].
% 2.74/3.01 2365 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(2163(a,1),4(a,1))].
% 2.74/3.01 2366 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),2163(a,1,1)),flip(a)].
% 2.74/3.01 2370 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(86(a,1),2163(a,1,1)),flip(a)].
% 2.74/3.01 2403 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(2365(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),35(7)])].
% 2.74/3.01 2417 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(2403(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 2.74/3.01 2493 meet(A,complement(join(A,B))) = zero. [para(4(a,1),2366(a,1,2)),rewrite([35(2)]),flip(a)].
% 2.74/3.01 2503 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(2366(a,1),2417(a,1,2))].
% 2.74/3.01 2506 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(2493(a,1),2163(a,1)),rewrite([8(3)]),flip(a)].
% 2.74/3.01 2511 meet(A,meet(B,meet(C,complement(meet(A,join(B,D)))))) = zero. [para(2503(a,1),10(a,2,2)),rewrite([7(5),10(5,R),7(4),35(8)])].
% 2.74/3.01 2512 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(2503(a,1),10(a,2)),rewrite([7(4)])].
% 2.74/3.01 2555 meet(A,meet(complement(B),join(meet(B,C),meet(B,D)))) = zero. [para(428(a,1),2506(a,1,2,2,1)),rewrite([7(5)])].
% 2.74/3.01 2583 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(2512(a,1),2366(a,1)),flip(a)].
% 2.74/3.01 3103 meet(A,meet(complement(A),join(B,complement(join(B,complement(A)))))) != zero | meet(A,join(B,complement(join(B,complement(A))))) = A. [para(1795(a,1),17(b,1)),rewrite([10(7,R),7(6),1421(14)]),flip(c),xx(b)].
% 2.74/3.01 3267 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [hyper(61,a,2555,a,b,1795,a),rewrite([8(32),3(32),7(22),1449(22),12(21,R),8(20),1082(21),7(7),2555(7),1421(8)]),flip(a)].
% 2.74/3.01 3328 join(join(A,B),meet(complement(A),complement(join(A,B)))) = one. [para(1472(a,1),146(a,1,2,2)),rewrite([7(5),86(5),3(4)]),flip(a)].
% 2.74/3.01 3346 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [hyper(75,a,37,a,b,3328,a),rewrite([3328(10),7(6),2370(6)])].
% 2.74/3.01 3354 meet(A,meet(B,meet(complement(A),join(C,D)))) = zero. [para(3328(a,1),2511(a,1,2,2,2,1,2)),rewrite([18(3),10(4,R)])].
% 2.74/3.01 3357 join(complement(A),complement(join(A,B))) = complement(A). [para(3346(a,1),6(a,1,2))].
% 2.74/3.01 3368 meet(A,complement(join(B,complement(A)))) = complement(join(B,complement(A))). [para(1421(a,1),3346(a,1,1)),rewrite([8(2),8(6)])].
% 2.74/3.01 3418 join(A,complement(join(B,complement(A)))) = A. [para(1421(a,1),3357(a,1,1)),rewrite([8(2),1421(6)])].
% 2.74/3.01 3429 join(A,meet(B,complement(join(C,complement(A))))) = A. [para(3418(a,1),26(a,1,2,2,2,2)),rewrite([7(4),6(5),7(4),3368(4),3418(4),7(4)]),flip(a)].
% 2.74/3.01 3504 meet(A,meet(complement(A),join(B,C))) = zero. [para(1(a,1),3354(a,1,2))].
% 2.74/3.01 3518 meet(A,join(B,complement(join(B,complement(A))))) = A. [back_rewrite(3103),rewrite([3504(7)]),xx(a)].
% 2.74/3.01 3607 join(A,complement(join(A,complement(B)))) = join(A,B). [para(3518(a,1),962(a,1,2,2)),rewrite([8(4),3418(4)]),flip(a)].
% 2.74/3.01 3618 join(A,meet(B,complement(A))) = join(A,B). [para(3607(a,1),58(a,1,2,2)),rewrite([58(4),7(8),3346(8),3607(7)])].
% 2.74/3.01 3630 join(A,complement(join(A,B))) = join(A,complement(B)). [para(1421(a,1),3607(a,1,2,1,2))].
% 2.74/3.01 3852 join(A,meet(B,meet(C,complement(A)))) = join(A,meet(B,C)). [para(26(a,1),3618(a,2)),rewrite([7(6),10(6,R),7(5),2167(7)])].
% 2.74/3.01 3854 join(A,meet(B,meet(complement(A),join(A,C)))) = join(A,meet(B,join(A,C))). [para(63(a,1),3618(a,2)),rewrite([7(7),330(8)])].
% 2.74/3.01 3859 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(1421(a,1),3618(a,1,2,2)),rewrite([7(2),8(5)])].
% 2.74/3.01 3863 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(2583(a,1),3618(a,1,2)),rewrite([8(5),704(5),8(7)]),flip(a)].
% 2.74/3.01 4288 join(A,complement(meet(B,complement(A)))) = join(A,complement(B)). [para(3618(a,1),3630(a,1,2,1)),rewrite([3630(3)]),flip(a)].
% 2.74/3.01 4433 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(3267(a,1),199(a,1,2,2,2)),rewrite([6(3),7(2),6(8),7(7),8(11),704(11),22(10),7(6),20(6),8(6),1862(6),6(6),7(5),7(10),10(10),7(9),4(9),35(9),8(9),704(9)]),flip(a)].
% 2.74/3.01 4499 join(complement(A),complement(join(B,A))) = complement(A). [para(3859(a,1),3429(a,1)),rewrite([1421(2),8(4)])].
% 2.74/3.01 4521 complement(meet(A,complement(B))) = join(B,complement(A)). [para(477(a,1),4499(a,1,2,1)),rewrite([1421(5),8(4),4288(4)]),flip(a)].
% 2.74/3.01 4549 complement(join(A,complement(B))) = meet(B,complement(A)). [para(4521(a,1),1421(a,1,1))].
% 2.74/3.01 4550 complement(meet(A,B)) = join(complement(A),complement(B)). [para(1421(a,1),4521(a,1,1,2)),rewrite([8(5)])].
% 2.74/3.01 4927 complement(join(A,B)) = meet(complement(A),complement(B)). [para(1421(a,1),4549(a,1,1,2)),rewrite([7(5)])].
% 2.74/3.01 4948 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(3630(a,1),4549(a,1,1)),rewrite([4927(3),1421(3),7(2),7(5)]),flip(a)].
% 2.74/3.01 5276 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [back_rewrite(3854),rewrite([4948(3),3852(4)]),flip(a)].
% 2.74/3.01 5544 meet(join(A,B),join(A,C)) = join(A,meet(B,C)). [back_rewrite(3863),rewrite([5276(4),7(2),5276(3),7(1)]),flip(a)].
% 2.74/3.01 5922 meet(complement(A),join(B,A)) = meet(B,complement(A)). [para(4948(a,1),7(a,1)),rewrite([8(3),7(5)]),flip(a)].
% 2.74/3.01 6053 meet(join(A,B),join(B,complement(A))) = B. [para(3618(a,1),5922(a,1,2)),rewrite([4550(3),1421(3),8(2),8(3),7(4),4550(7),1421(7),8(6),5(7)])].
% 2.74/3.01 6061 meet(A,join(B,A)) = A. [para(6053(a,1),20(a,1,2)),rewrite([7(2),6053(6)])].
% 2.74/3.01 6442 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [para(5276(a,1),6061(a,1,2)),rewrite([2164(5),5544(4),10(2,R),1(1)])].
% 2.74/3.01 6539 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(4433),rewrite([6442(4),8(2),6442(3),8(1)]),flip(a)].
% 2.74/3.01 6540 $F # answer(prove_distributivity). [resolve(6539,a,16,a)].
% 2.74/3.01
% 2.74/3.01 % SZS output end Refutation
% 2.74/3.01 ============================== end of proof ==========================
% 2.74/3.01
% 2.74/3.01 ============================== STATISTICS ============================
% 2.74/3.01
% 2.74/3.01 Given=357. Generated=56069. Kept=6535. proofs=1.
% 2.74/3.01 Usable=153. Sos=1147. Demods=994. Limbo=97, Disabled=5150. Hints=0.
% 2.74/3.01 Megabytes=7.46.
% 2.74/3.01 User_CPU=2.00, System_CPU=0.04, Wall_clock=2.
% 2.74/3.01
% 2.74/3.01 ============================== end of statistics =====================
% 2.74/3.01
% 2.74/3.01 ============================== end of search =========================
% 2.74/3.01
% 2.74/3.01 THEOREM PROVED
% 2.74/3.01 % SZS status Unsatisfiable
% 2.74/3.01
% 2.74/3.01 Exiting with 1 proof.
% 2.74/3.01
% 2.74/3.01 Process 11781 exit (max_proofs) Thu Jun 30 07:02:25 2022
% 2.74/3.01 Prover9 interrupted
%------------------------------------------------------------------------------