TSTP Solution File: LAT020-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT020-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:25:08 EDT 2022
% Result : Unsatisfiable 1.97s 2.26s
% Output : Refutation 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT020-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.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 13:26:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.97/2.26 ============================== Prover9 ===============================
% 1.97/2.26 Prover9 (32) version 2009-11A, November 2009.
% 1.97/2.26 Process 22164 was started by sandbox2 on n029.cluster.edu,
% 1.97/2.26 Thu Jun 30 13:26:39 2022
% 1.97/2.26 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22011_n029.cluster.edu".
% 1.97/2.26 ============================== end of head ===========================
% 1.97/2.26
% 1.97/2.26 ============================== INPUT =================================
% 1.97/2.26
% 1.97/2.26 % Reading from file /tmp/Prover9_22011_n029.cluster.edu
% 1.97/2.26
% 1.97/2.26 set(prolog_style_variables).
% 1.97/2.26 set(auto2).
% 1.97/2.26 % set(auto2) -> set(auto).
% 1.97/2.26 % set(auto) -> set(auto_inference).
% 1.97/2.26 % set(auto) -> set(auto_setup).
% 1.97/2.26 % set(auto_setup) -> set(predicate_elim).
% 1.97/2.26 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.97/2.26 % set(auto) -> set(auto_limits).
% 1.97/2.26 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.97/2.26 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.97/2.26 % set(auto) -> set(auto_denials).
% 1.97/2.26 % set(auto) -> set(auto_process).
% 1.97/2.26 % set(auto2) -> assign(new_constants, 1).
% 1.97/2.26 % set(auto2) -> assign(fold_denial_max, 3).
% 1.97/2.26 % set(auto2) -> assign(max_weight, "200.000").
% 1.97/2.26 % set(auto2) -> assign(max_hours, 1).
% 1.97/2.26 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.97/2.26 % set(auto2) -> assign(max_seconds, 0).
% 1.97/2.26 % set(auto2) -> assign(max_minutes, 5).
% 1.97/2.26 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.97/2.26 % set(auto2) -> set(sort_initial_sos).
% 1.97/2.26 % set(auto2) -> assign(sos_limit, -1).
% 1.97/2.26 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.97/2.26 % set(auto2) -> assign(max_megs, 400).
% 1.97/2.26 % set(auto2) -> assign(stats, some).
% 1.97/2.26 % set(auto2) -> clear(echo_input).
% 1.97/2.26 % set(auto2) -> set(quiet).
% 1.97/2.26 % set(auto2) -> clear(print_initial_clauses).
% 1.97/2.26 % set(auto2) -> clear(print_given).
% 1.97/2.26 assign(lrs_ticks,-1).
% 1.97/2.26 assign(sos_limit,10000).
% 1.97/2.26 assign(order,kbo).
% 1.97/2.26 set(lex_order_vars).
% 1.97/2.26 clear(print_given).
% 1.97/2.26
% 1.97/2.26 % formulas(sos). % not echoed (10 formulas)
% 1.97/2.26
% 1.97/2.26 ============================== end of input ==========================
% 1.97/2.26
% 1.97/2.26 % From the command line: assign(max_seconds, 300).
% 1.97/2.26
% 1.97/2.26 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.97/2.26
% 1.97/2.26 % Formulas that are not ordinary clauses:
% 1.97/2.26
% 1.97/2.26 ============================== end of process non-clausal formulas ===
% 1.97/2.26
% 1.97/2.26 ============================== PROCESS INITIAL CLAUSES ===============
% 1.97/2.26
% 1.97/2.26 ============================== PREDICATE ELIMINATION =================
% 1.97/2.26
% 1.97/2.26 ============================== end predicate elimination =============
% 1.97/2.26
% 1.97/2.26 Auto_denials:
% 1.97/2.26 % copying label prove_distributivity to answer in negative clause
% 1.97/2.26
% 1.97/2.26 Term ordering decisions:
% 1.97/2.26 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 1.97/2.26
% 1.97/2.26 ============================== end of process initial clauses ========
% 1.97/2.26
% 1.97/2.26 ============================== CLAUSES FOR SEARCH ====================
% 1.97/2.26
% 1.97/2.26 ============================== end of clauses for search =============
% 1.97/2.26
% 1.97/2.26 ============================== SEARCH ================================
% 1.97/2.26
% 1.97/2.26 % Starting search at 0.01 seconds.
% 1.97/2.26
% 1.97/2.26 ============================== PROOF =================================
% 1.97/2.26 % SZS status Unsatisfiable
% 1.97/2.26 % SZS output start Refutation
% 1.97/2.26
% 1.97/2.26 % Proof 1 at 1.29 (+ 0.01) seconds: prove_distributivity.
% 1.97/2.26 % Length of proof is 169.
% 1.97/2.26 % Level of proof is 30.
% 1.97/2.26 % Maximum clause weight is 37.000.
% 1.97/2.26 % Given clauses 97.
% 1.97/2.26
% 1.97/2.26 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.97/2.26 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.97/2.26 3 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.97/2.26 4 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.97/2.26 5 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.97/2.26 6 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(5),rewrite([3(2)]),flip(a)].
% 1.97/2.26 7 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.97/2.26 8 join(A,join(B,C)) = join(C,join(A,B)). [copy(7),rewrite([4(2)]),flip(a)].
% 1.97/2.26 9 join(meet(A,join(B,C)),meet(A,B)) = meet(A,join(B,C)) # label(quasi_lattice1) # label(axiom). [assumption].
% 1.97/2.26 10 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [copy(9),rewrite([4(4)])].
% 1.97/2.26 11 meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)) # label(quasi_lattice2) # label(axiom). [assumption].
% 1.97/2.26 12 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [copy(11),rewrite([3(4)])].
% 1.97/2.26 13 join(meet(join(meet(A,B),C),B),meet(C,A)) = meet(join(meet(join(A,B),C),B),join(C,A)) # label(self_dual_distributivity) # label(hypothesis). [assumption].
% 1.97/2.26 14 meet(join(A,B),join(C,meet(B,join(A,C)))) = join(meet(A,B),meet(C,join(B,meet(A,C)))). [copy(13),rewrite([4(2),3(3),3(4),4(5),3(7),4(8),4(9),3(10)]),flip(a)].
% 1.97/2.26 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 1.97/2.26 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 1.97/2.26 17 meet(A,meet(A,B)) = meet(A,B). [para(6(a,1),1(a,1)),rewrite([3(1),3(2),6(2,R),1(1),3(3)])].
% 1.97/2.26 18 join(A,join(A,B)) = join(A,B). [para(8(a,1),2(a,1)),rewrite([4(1),4(2),8(2,R),2(1),4(3)])].
% 1.97/2.26 20 join(join(A,B),meet(A,join(A,B))) = join(A,B). [para(1(a,1),10(a,1,2)),rewrite([3(2),4(4),1(7)])].
% 1.97/2.27 21 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(3(a,1),10(a,1,1))].
% 1.97/2.27 22 join(meet(A,meet(B,C)),meet(B,join(D,meet(A,C)))) = meet(B,join(D,meet(A,C))). [para(6(a,1),10(a,1,1)),rewrite([3(3),4(4),3(7),4(8)])].
% 1.97/2.27 23 join(meet(A,meet(B,C)),meet(C,join(D,meet(A,B)))) = meet(C,join(D,meet(A,B))). [para(6(a,2),10(a,1,1)),rewrite([4(4),4(8)])].
% 1.97/2.27 26 meet(meet(A,B),join(A,meet(A,B))) = meet(A,B). [para(2(a,1),12(a,1,2)),rewrite([4(2),3(4),2(7)])].
% 1.97/2.27 27 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(4(a,1),12(a,1,1))].
% 1.97/2.27 28 meet(join(A,join(B,C)),join(B,meet(D,join(A,C)))) = join(B,meet(D,join(A,C))). [para(8(a,1),12(a,1,1)),rewrite([4(3),3(4),4(7),3(8)])].
% 1.97/2.27 29 meet(join(A,join(B,C)),join(C,meet(D,join(A,B)))) = join(C,meet(D,join(A,B))). [para(8(a,2),12(a,1,1)),rewrite([3(4),3(8)])].
% 1.97/2.27 31 join(A,join(meet(B,C),meet(A,join(A,B)))) = join(A,meet(B,C)). [para(12(a,1),10(a,1,2)),rewrite([3(2),8(5,R),12(9)])].
% 1.97/2.27 32 meet(meet(A,join(B,C)),join(meet(A,B),meet(A,meet(D,join(B,C))))) = join(meet(A,B),meet(A,meet(D,join(B,C)))). [para(10(a,1),12(a,1,1)),rewrite([3(6),6(6,R),3(5),3(12),6(12,R),3(11)])].
% 1.97/2.27 33 meet(A,meet(join(B,C),join(A,meet(A,B)))) = meet(A,join(B,C)). [para(10(a,1),12(a,1,2)),rewrite([4(2),6(5,R),10(9)])].
% 1.97/2.27 34 meet(join(A,join(B,C)),join(A,join(B,meet(C,D)))) = join(A,join(B,meet(C,D))). [para(12(a,1),12(a,1,2,2)),rewrite([12(10)])].
% 1.97/2.27 37 meet(join(A,B),join(A,meet(A,B))) = join(meet(A,B),meet(A,join(A,B))). [para(1(a,1),14(a,2,2,2,2)),rewrite([2(2),3(2),4(6)])].
% 1.97/2.27 39 meet(join(A,B),join(C,meet(A,join(C,B)))) = join(meet(A,B),meet(C,join(A,meet(C,B)))). [para(14(a,1),3(a,2)),rewrite([4(1),4(4),3(5),3(6),3(7)])].
% 1.97/2.27 40 meet(join(A,B),join(C,meet(A,join(B,C)))) = join(meet(A,B),meet(C,join(A,meet(B,C)))). [para(4(a,1),14(a,1,1)),rewrite([3(6)])].
% 1.97/2.27 44 join(meet(A,B),join(meet(C,join(A,B)),meet(C,join(B,meet(A,C))))) = join(meet(A,B),meet(C,join(B,meet(A,C)))). [para(14(a,1),10(a,1,2)),rewrite([3(2),8(8,R),4(7),14(13)])].
% 1.97/2.27 47 join(meet(A,B),meet(meet(A,B),join(B,meet(A,B)))) = meet(B,join(meet(A,B),meet(A,join(A,B)))). [para(10(a,1),14(a,1,2)),rewrite([3(2),6(5,R),3(4),37(4),3(7),3(8),17(9)]),flip(a)].
% 1.97/2.27 48 join(meet(A,B),meet(A,join(A,B))) = meet(A,join(A,B)). [para(10(a,1),14(a,2)),rewrite([2(2),3(2),37(4),1(5),4(5)])].
% 1.97/2.27 50 meet(A,join(A,B)) = join(A,meet(A,B)). [para(14(a,1),12(a,1)),rewrite([1(2),4(2),48(4),2(3),3(3)])].
% 1.97/2.27 59 join(meet(A,B),meet(meet(A,B),join(B,meet(A,B)))) = meet(B,join(A,meet(A,B))). [back_rewrite(47),rewrite([50(9),8(10,R),2(9)])].
% 1.97/2.27 60 meet(join(A,B),join(A,meet(A,B))) = join(A,meet(A,B)). [back_rewrite(37),rewrite([50(7),8(8,R),2(7)])].
% 1.97/2.27 65 join(A,join(meet(A,B),meet(B,C))) = join(A,meet(B,C)). [back_rewrite(31),rewrite([50(3),8(4,R),18(5)])].
% 1.97/2.27 66 join(A,join(join(A,B),meet(A,B))) = join(A,B). [back_rewrite(20),rewrite([50(3),8(4,R),4(3)])].
% 1.97/2.27 67 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(17(a,1),10(a,1,1)),rewrite([4(3),4(7)])].
% 1.97/2.27 69 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(18(a,1),12(a,1,1)),rewrite([3(3),3(7)])].
% 1.97/2.27 72 meet(A,join(B,meet(B,C))) = meet(B,meet(A,join(B,C))). [para(50(a,1),6(a,2,2)),rewrite([3(2)]),flip(a)].
% 1.97/2.27 76 meet(meet(A,B),join(B,meet(A,B))) = meet(A,B). [para(3(a,1),26(a,1,1)),rewrite([3(2),3(5)])].
% 1.97/2.27 84 meet(A,join(B,meet(B,A))) = meet(B,A). [back_rewrite(59),rewrite([76(5),2(3)]),flip(a)].
% 1.97/2.27 87 meet(A,meet(B,join(C,meet(A,C)))) = meet(A,meet(C,B)). [para(84(a,1),6(a,2,2)),rewrite([3(1),3(3),3(5),6(6),3(5),6(6,R),3(5)])].
% 1.97/2.27 107 join(join(A,B),meet(A,B)) = join(A,B). [para(66(a,1),8(a,1)),rewrite([18(4),4(4)]),flip(a)].
% 1.97/2.27 115 meet(join(A,B),join(C,meet(meet(A,B),join(A,join(B,C))))) = join(meet(A,B),meet(C,join(meet(A,B),meet(C,join(A,B))))). [para(107(a,1),14(a,1,1)),rewrite([4(4),8(4),4(3),8(4,R),4(3),6(10),3(9),50(9),84(10),3(11)])].
% 1.97/2.27 117 join(join(A,meet(A,B)),meet(B,join(A,B))) = join(A,B). [para(107(a,1),14(a,2,2,2)),rewrite([18(2),1(4),8(3,R),2(2),1(3),50(3)]),flip(a)].
% 1.97/2.27 139 meet(A,join(B,A)) = join(A,meet(B,A)). [para(22(a,1),14(a,2)),rewrite([1(1),1(2),84(5),1(3),50(5),6(4,R),1(3)])].
% 1.97/2.27 156 join(A,join(B,meet(A,B))) = join(A,B). [back_rewrite(117),rewrite([139(4),8(5),4(4),8(4,R),4(3),8(5,R),4(4),8(4,R),2(3)])].
% 1.97/2.27 158 meet(join(A,B),join(A,join(B,C))) = join(join(A,B),meet(C,join(A,B))). [para(8(a,1),139(a,1,2)),rewrite([4(2),8(3,R),4(2)])].
% 1.97/2.27 159 join(join(A,B),meet(meet(B,C),join(A,B))) = join(A,join(B,meet(B,C))). [para(139(a,1),12(a,1,2,2)),rewrite([3(2),158(5),4(6),50(7)])].
% 1.97/2.27 161 join(A,join(B,join(C,meet(A,B)))) = join(A,join(B,C)). [para(156(a,1),8(a,2,2)),rewrite([4(3),8(3,R),4(2),8(6),4(5),8(6,R),4(5)])].
% 1.97/2.27 168 join(A,join(meet(B,A),meet(B,C))) = join(A,meet(B,C)). [para(27(a,1),10(a,1,2)),rewrite([3(2),139(2),8(5,R),8(4,R),18(5),27(8)])].
% 1.97/2.27 174 join(join(A,B),meet(C,join(A,meet(A,B)))) = join(join(A,B),meet(A,C)). [para(18(a,1),27(a,1,1)),rewrite([50(5),6(4),3(3),50(3)])].
% 1.97/2.27 175 join(join(A,B),meet(meet(A,C),join(A,B))) = join(A,join(B,meet(A,C))). [para(27(a,1),50(a,2,2)),rewrite([8(5,R),8(4),4(3),8(4,R),4(3),8(5,R),4(4),18(4),158(5),8(9,R),8(8),4(7),8(8,R),4(7),8(9,R),4(8),18(8)])].
% 1.97/2.27 181 meet(join(A,join(B,C)),join(A,join(B,meet(B,C)))) = join(A,join(B,meet(B,C))). [para(60(a,1),12(a,1,2,2)),rewrite([60(10)])].
% 1.97/2.27 207 join(A,join(meet(B,C),meet(A,B))) = join(A,meet(B,C)). [para(4(a,1),65(a,1,2))].
% 1.97/2.27 217 join(A,join(meet(A,B),meet(A,meet(B,C)))) = join(A,meet(A,meet(B,C))). [para(17(a,1),65(a,1,2,1)),rewrite([3(3),6(3),3(2),6(3,R),3(2),3(7),6(7),3(6),6(7,R),3(6)])].
% 1.97/2.27 238 meet(A,meet(B,join(A,meet(A,C)))) = meet(A,meet(B,join(A,C))). [para(72(a,2),17(a,1,2))].
% 1.97/2.27 242 join(meet(A,B),meet(A,meet(B,join(A,C)))) = meet(B,join(A,meet(A,C))). [para(72(a,1),21(a,1,2))].
% 1.97/2.27 250 meet(join(A,meet(A,B)),join(A,join(C,meet(A,B)))) = join(join(A,meet(A,B)),meet(A,meet(C,join(A,B)))). [para(72(a,1),139(a,2,2)),rewrite([8(5,R),4(4)])].
% 1.97/2.27 261 meet(A,meet(join(B,C),join(A,B))) = meet(A,join(B,C)). [back_rewrite(33),rewrite([238(5)])].
% 1.97/2.27 308 join(A,join(B,join(C,meet(A,C)))) = join(A,join(B,C)). [para(161(a,1),4(a,2)),rewrite([3(1),4(4),8(4,R),4(3),8(3,R),4(2),8(6),4(5),8(6,R),4(5)])].
% 1.97/2.27 310 join(A,join(join(B,C),meet(A,B))) = join(A,join(B,C)). [para(10(a,1),161(a,1,2,2)),rewrite([156(5)]),flip(a)].
% 1.97/2.27 322 join(A,join(meet(B,C),meet(B,A))) = join(A,meet(B,C)). [para(168(a,1),8(a,2)),rewrite([4(3),8(4,R)])].
% 1.97/2.27 325 join(join(A,meet(A,B)),meet(B,C)) = join(A,meet(B,C)). [para(84(a,1),168(a,1,2,1)),rewrite([8(6,R),8(5,R),65(5),8(4,R),207(4)]),flip(a)].
% 1.97/2.27 331 join(A,join(meet(B,C),meet(A,C))) = join(A,meet(B,C)). [para(3(a,1),207(a,1,2,1)),rewrite([3(5)])].
% 1.97/2.27 342 join(A,meet(A,join(meet(B,C),meet(A,B)))) = join(A,meet(A,meet(B,C))). [para(207(a,1),50(a,1,2)),rewrite([50(3)]),flip(a)].
% 1.97/2.27 353 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(261(a,1),3(a,2)),rewrite([4(2),3(4)])].
% 1.97/2.27 355 meet(A,meet(join(B,C),join(A,C))) = meet(A,join(B,C)). [para(4(a,1),261(a,1,2,1)),rewrite([4(5)])].
% 1.97/2.27 357 meet(join(A,B),join(C,meet(A,C))) = meet(C,join(A,B)). [para(261(a,1),6(a,2)),rewrite([4(2),3(3),139(3)])].
% 1.97/2.27 364 meet(A,join(join(A,B),meet(C,join(A,B)))) = join(A,meet(A,join(B,C))). [para(18(a,1),261(a,1,2,2)),rewrite([4(2),8(2),4(1),8(2,R),4(1),3(4),158(4),4(7),8(7),4(6),8(7,R),4(6),50(8)])].
% 1.97/2.27 380 meet(A,meet(join(A,B),join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(72(a,1),261(a,1,2)),rewrite([4(2),3(4),17(6),4(7)])].
% 1.97/2.27 454 join(join(A,join(B,meet(B,C))),meet(C,join(A,join(B,meet(B,C))))) = join(A,join(B,meet(B,C))). [para(308(a,1),139(a,1,2)),rewrite([3(1),8(5),4(4),8(5,R),4(4),3(6),181(6),3(4),3(7)]),flip(a)].
% 1.97/2.27 483 join(join(A,B),meet(C,join(A,B))) = join(join(A,B),meet(A,C)). [para(10(a,1),322(a,1,2)),rewrite([3(6)])].
% 1.97/2.27 498 join(A,join(join(B,meet(B,C)),meet(A,C))) = join(A,join(B,meet(B,C))). [back_rewrite(454),rewrite([483(8),4(5),8(5,R)])].
% 1.97/2.27 503 meet(A,join(join(A,B),meet(A,C))) = join(A,meet(A,join(B,C))). [back_rewrite(364),rewrite([483(4)])].
% 1.97/2.27 509 join(join(A,B),meet(A,C)) = join(A,join(B,meet(A,C))). [back_rewrite(175),rewrite([483(5),17(3)])].
% 1.97/2.27 510 join(A,join(B,meet(A,meet(B,C)))) = join(A,join(B,meet(B,C))). [back_rewrite(159),rewrite([483(5),509(4)])].
% 1.97/2.27 511 meet(join(A,B),join(A,join(B,C))) = join(A,join(B,meet(A,C))). [back_rewrite(158),rewrite([483(8),509(7)])].
% 1.97/2.27 526 join(A,meet(A,join(B,meet(A,C)))) = join(A,meet(A,join(B,C))). [back_rewrite(503),rewrite([509(3),50(4)])].
% 1.97/2.27 530 join(join(A,B),meet(C,join(A,B))) = join(A,join(B,meet(A,C))). [back_rewrite(483),rewrite([509(7)])].
% 1.97/2.27 536 meet(join(A,meet(A,B)),join(A,join(C,meet(A,B)))) = join(A,join(meet(A,B),meet(A,meet(C,join(A,B))))). [back_rewrite(250),rewrite([509(12)])].
% 1.97/2.27 538 join(join(A,B),meet(C,join(A,meet(A,B)))) = join(A,join(B,meet(A,C))). [back_rewrite(174),rewrite([509(8)])].
% 1.97/2.27 546 join(A,meet(A,join(B,meet(B,C)))) = join(A,meet(A,meet(B,C))). [back_rewrite(342),rewrite([526(5),4(2)])].
% 1.97/2.27 566 meet(A,join(B,join(C,meet(A,B)))) = meet(A,join(B,C)). [para(29(a,1),87(a,1,2)),rewrite([530(4),3(1),8(7,R),2(6),18(7),1(7)])].
% 1.97/2.27 593 join(join(A,meet(B,A)),meet(B,C)) = join(A,meet(B,C)). [para(325(a,1),27(a,1,2)),rewrite([3(1),156(3),27(4),3(3)]),flip(a)].
% 1.97/2.27 615 join(A,join(meet(B,C),meet(C,A))) = join(A,meet(B,C)). [para(331(a,1),4(a,2)),rewrite([3(2),4(4)])].
% 1.97/2.27 624 join(A,meet(A,join(B,meet(C,B)))) = join(A,meet(A,meet(C,B))). [para(331(a,1),50(a,1,2)),rewrite([50(3),526(8),4(5)]),flip(a)].
% 1.97/2.27 637 join(A,join(meet(A,B),meet(C,B))) = join(A,meet(C,B)). [para(331(a,1),310(a,2)),rewrite([4(6),8(6),4(5),308(7)])].
% 1.97/2.27 643 join(meet(A,B),meet(A,meet(B,C))) = meet(meet(A,B),join(A,C)). [para(12(a,1),353(a,1,2)),rewrite([139(4),6(3),3(2),6(3,R),3(2),4(6)])].
% 1.97/2.27 662 meet(meet(A,B),join(A,C)) = meet(B,join(A,meet(A,C))). [back_rewrite(242),rewrite([643(5),18(3)])].
% 1.97/2.27 663 join(A,meet(B,join(A,meet(A,C)))) = join(A,meet(A,meet(B,C))). [back_rewrite(217),rewrite([643(4),662(3)])].
% 1.97/2.27 668 join(meet(A,B),meet(A,meet(B,C))) = meet(B,join(A,meet(A,C))). [back_rewrite(643),rewrite([662(7)])].
% 1.97/2.27 669 meet(join(A,B),join(C,meet(B,join(A,meet(A,join(B,C)))))) = join(meet(A,B),meet(C,join(meet(A,B),meet(C,join(A,B))))). [back_rewrite(115),rewrite([662(5)])].
% 1.97/2.27 751 meet(A,meet(join(B,C),join(C,A))) = meet(A,join(B,C)). [para(355(a,1),3(a,2)),rewrite([4(2),3(4)])].
% 1.97/2.27 753 meet(join(A,B),join(C,meet(B,C))) = meet(C,join(A,B)). [para(355(a,1),6(a,2)),rewrite([4(2),3(3),139(3)])].
% 1.97/2.27 780 meet(join(A,meet(A,B)),join(B,C)) = meet(A,join(B,C)). [para(357(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 1.97/2.27 789 meet(join(A,meet(B,A)),join(B,C)) = meet(A,join(B,C)). [para(84(a,1),357(a,1,2,2)),rewrite([3(2),3(4),4(5),8(5,R),2(4),357(4),3(3)]),flip(a)].
% 1.97/2.27 807 meet(A,join(B,join(C,meet(B,A)))) = meet(A,join(B,C)). [para(357(a,1),261(a,2)),rewrite([4(5),8(5),4(4),8(5,R),4(4),789(6),6(5,R),3(4),511(4)])].
% 1.97/2.27 812 join(join(A,meet(A,join(B,C))),meet(D,join(B,C))) = join(A,meet(D,join(B,C))). [para(357(a,1),325(a,1,2)),rewrite([357(10)])].
% 1.97/2.27 860 join(join(A,B),meet(B,C)) = join(A,join(B,meet(B,C))). [para(4(a,1),509(a,1,1)),rewrite([8(6,R),4(5)])].
% 1.97/2.27 867 meet(join(A,B),join(B,join(C,meet(B,join(A,join(B,C)))))) = join(B,meet(A,join(B,C))). [para(509(a,1),14(a,1,2)),rewrite([69(13),8(12,R),4(11),10(11)])].
% 1.97/2.27 871 meet(A,join(B,meet(B,join(A,C)))) = meet(A,join(B,meet(B,C))). [para(509(a,1),139(a,1,2)),rewrite([662(5),526(4),4(1),6(8),3(7),50(7),21(9)])].
% 1.97/2.27 875 join(join(A,B),meet(C,join(A,meet(A,D)))) = join(A,join(B,meet(A,meet(C,join(A,D))))). [para(72(a,2),509(a,1,2))].
% 1.97/2.27 908 join(meet(A,B),meet(C,join(meet(A,B),meet(C,join(A,B))))) = meet(join(A,B),join(C,meet(B,join(A,meet(A,C))))). [back_rewrite(669),rewrite([871(5)]),flip(a)].
% 1.97/2.27 910 join(A,join(B,meet(A,meet(C,join(A,B))))) = join(A,join(B,meet(A,C))). [back_rewrite(538),rewrite([875(5)])].
% 1.97/2.27 960 meet(join(A,meet(A,B)),join(A,meet(A,join(B,C)))) = join(A,meet(A,join(B,C))). [para(261(a,1),32(a,1,2,2)),rewrite([50(2),1(3),1(7),261(10)])].
% 1.97/2.27 1010 meet(join(A,B),join(C,join(D,meet(A,C)))) = meet(join(A,B),join(C,D)). [para(357(a,1),566(a,1,2,2,2)),rewrite([8(7,R),8(6),4(5),8(6,R),4(5),21(5),8(5,R),4(4),807(6),4(7),8(7,R),4(6)]),flip(a)].
% 1.97/2.27 1021 join(meet(A,join(B,meet(B,C))),meet(C,D)) = join(meet(B,A),meet(C,D)). [para(6(a,1),593(a,1,1,2)),rewrite([3(2),6(3,R),3(2),668(4)])].
% 1.97/2.27 1027 join(join(A,meet(A,B)),meet(C,join(B,D))) = join(A,meet(C,join(B,D))). [para(357(a,1),593(a,1,1,2)),rewrite([3(1),509(5),10(4),3(5),812(6),3(4),3(7)]),flip(a)].
% 1.97/2.27 1031 join(meet(A,B),join(meet(C,D),meet(A,meet(B,D)))) = join(meet(A,B),meet(C,D)). [para(6(a,1),615(a,1,2,2)),rewrite([3(3),6(4,R),3(3)])].
% 1.97/2.27 1098 meet(join(A,meet(B,C)),join(A,join(D,meet(B,C)))) = meet(join(A,meet(B,C)),join(A,join(B,D))). [para(34(a,1),353(a,1,2)),rewrite([8(5,R),4(4),8(10),4(9),8(10,R),4(9)])].
% 1.97/2.27 1120 join(A,join(meet(A,B),meet(A,meet(C,join(A,B))))) = meet(join(A,meet(A,B)),join(A,C)). [back_rewrite(536),rewrite([1098(6),18(4)]),flip(a)].
% 1.97/2.27 1128 meet(meet(A,B),join(B,C)) = meet(A,join(B,meet(B,C))). [para(3(a,1),662(a,1,1))].
% 1.97/2.27 1138 meet(join(A,meet(A,B)),join(A,C)) = meet(join(A,B),join(A,meet(A,C))). [para(50(a,1),662(a,1,1))].
% 1.97/2.27 1148 join(A,join(join(B,C),meet(A,D))) = join(A,join(B,join(C,meet(A,D)))). [para(662(a,1),161(a,1,2,2,2)),rewrite([8(7,R),4(6),875(6),910(6),8(5,R),4(4),8(4,R),4(3),8(6,R),4(5),8(5,R),4(4),8(4,R),2(3),4(7),8(7),4(6),8(7,R),4(6),8(8,R)]),flip(a)].
% 1.97/2.27 1157 join(meet(A,join(B,meet(B,C))),meet(D,join(B,C))) = join(meet(B,A),meet(D,join(B,C))). [para(662(a,1),325(a,1,1,2)),rewrite([21(5),3(5),3(9)])].
% 1.97/2.27 1159 join(A,join(meet(B,C),meet(A,join(C,D)))) = join(A,meet(B,join(C,meet(C,D)))). [para(662(a,1),331(a,1,2,1)),rewrite([1157(6),3(1),3(6),1128(8)])].
% 1.97/2.27 1160 join(A,join(meet(B,C),meet(A,join(B,D)))) = join(A,meet(C,join(B,meet(B,D)))). [para(662(a,1),331(a,2,2)),rewrite([662(3),1157(6)])].
% 1.97/2.27 1174 join(A,join(B,meet(C,join(A,meet(A,D))))) = join(A,join(B,meet(A,meet(C,D)))). [para(662(a,1),593(a,1,1,2)),rewrite([875(5),910(5),3(5),6(5),3(4),6(5,R),3(4),509(6),1148(6),668(4),3(8),6(8),3(7),6(8,R),3(7),509(9)])].
% 1.97/2.27 1182 join(A,join(meet(A,B),meet(A,meet(C,join(A,B))))) = meet(join(A,B),join(A,meet(A,C))). [back_rewrite(1120),rewrite([1138(10)])].
% 1.97/2.27 1183 meet(join(A,B),join(A,meet(A,join(B,C)))) = join(A,meet(A,join(B,C))). [back_rewrite(960),rewrite([1138(6),17(4)])].
% 1.97/2.27 1209 join(A,join(B,meet(B,C))) = join(A,join(B,meet(A,C))). [back_rewrite(498),rewrite([1148(5),637(4)]),flip(a)].
% 1.97/2.27 1253 meet(join(A,join(B,meet(B,join(A,C)))),join(C,meet(A,join(B,meet(A,meet(B,C)))))) = join(meet(B,join(A,C)),meet(C,join(A,join(B,meet(B,C))))). [para(14(a,1),39(a,1,2,2)),rewrite([860(4),1159(10),6(6,R),3(5),6(14,R),353(14),6(16,R),3(15),139(15),860(17),624(16),6(14,R),3(13),510(16)])].
% 1.97/2.27 1272 join(meet(A,B),meet(C,join(A,join(C,meet(C,B))))) = join(C,meet(A,B)). [para(27(a,1),39(a,1,2,2)),rewrite([509(3),18(6),3(6),139(6),530(6),3(2),322(4),6(5),3(4),50(4),6(8,R),3(7),509(9),510(9),1021(10)]),flip(a)].
% 1.97/2.27 1361 meet(meet(A,B),join(C,A)) = meet(B,join(A,meet(C,A))). [para(17(a,1),753(a,1,2,2)),rewrite([2(4),6(3),3(2),139(2)]),flip(a)].
% 1.97/2.27 1364 meet(join(A,B),join(C,meet(C,B))) = meet(C,join(A,B)). [para(753(a,1),21(a,1,2)),rewrite([2(5),3(4)]),flip(a)].
% 1.97/2.27 1385 meet(join(A,meet(B,A)),join(C,join(B,D))) = meet(A,join(C,join(B,D))). [para(357(a,1),753(a,1,2,2)),rewrite([509(7),21(6),1364(6)]),flip(a)].
% 1.97/2.27 1393 meet(A,join(B,join(C,meet(C,A)))) = meet(A,join(B,C)). [para(753(a,1),751(a,2)),rewrite([8(6),4(5),8(6,R),4(5),1385(7),6(6,R),3(5),511(5),510(4)])].
% 1.97/2.27 1399 meet(join(A,join(B,meet(B,join(A,C)))),join(C,meet(A,join(B,meet(A,meet(B,C)))))) = join(meet(B,join(A,C)),meet(C,join(A,B))). [back_rewrite(1253),rewrite([1393(16)])].
% 1.97/2.27 1406 meet(join(A,meet(A,B)),join(C,meet(A,B))) = meet(A,join(C,meet(A,B))). [para(17(a,1),780(a,1,1,2)),rewrite([4(4),4(7)])].
% 1.97/2.27 1426 meet(join(A,join(B,meet(A,C))),join(C,D)) = meet(join(A,B),join(C,D)). [para(357(a,1),780(a,1,1,2)),rewrite([530(4),4(6),8(6,R),4(5),1010(7),4(9),8(9,R),4(8),1010(10)])].
% 1.97/2.27 1448 meet(join(A,B),join(C,join(D,meet(C,A)))) = meet(join(C,D),join(A,B)). [para(789(a,1),357(a,1,2,2)),rewrite([3(1),4(3),8(3,R),4(2),530(7),3(4),1010(7),1426(5),3(5),4(7),8(7,R),4(6)]),flip(a)].
% 1.97/2.27 1461 meet(A,meet(join(A,B),join(C,B))) = meet(A,join(C,B)). [para(807(a,1),355(a,2)),rewrite([3(1),3(4),1448(7),1010(5)])].
% 1.97/2.27 1519 join(join(A,meet(B,C)),meet(B,meet(C,D))) = join(A,meet(C,join(B,meet(B,D)))). [para(325(a,1),860(a,1,1)),rewrite([3(4),6(4),3(3),6(4,R),3(3),3(10),6(10),3(9),6(10,R),3(9),668(11),1027(11)])].
% 1.97/2.27 1526 join(A,join(B,meet(A,meet(C,join(A,D))))) = join(A,join(B,meet(A,meet(C,D)))). [para(509(a,1),860(a,1,1)),rewrite([3(5),6(5),3(4),6(5,R),3(4),509(6),1519(5),1174(5),3(8),6(8),3(7),6(8,R),3(7),668(9),875(9)]),flip(a)].
% 1.97/2.27 1540 meet(join(A,B),join(A,meet(A,C))) = join(A,meet(A,meet(B,C))). [back_rewrite(1182),rewrite([1526(6),3(2),668(4),663(4)]),flip(a)].
% 1.97/2.27 1542 join(join(A,B),meet(C,join(A,meet(A,D)))) = join(A,join(B,meet(A,meet(C,D)))). [back_rewrite(875),rewrite([1526(10)])].
% 1.97/2.27 1547 join(A,meet(A,meet(B,C))) = join(A,meet(A,join(B,C))). [back_rewrite(1183),rewrite([1540(5),50(2),546(4)])].
% 1.97/2.27 1690 meet(A,join(B,join(A,C))) = join(A,meet(A,join(B,C))). [para(28(a,1),1128(a,2)),rewrite([3(3),8(5,R),4(4),3(6),6(6,R),1(5)])].
% 1.97/2.27 1713 meet(join(A,meet(B,A)),join(C,meet(B,join(A,meet(A,C))))) = join(meet(B,A),meet(C,join(meet(B,A),meet(A,C)))). [para(1128(a,1),40(a,1,2,2)),rewrite([4(2),3(9),6(9,R),1(8)])].
% 1.97/2.27 1724 join(A,meet(B,join(C,meet(C,A)))) = join(A,meet(C,B)). [back_rewrite(1272),rewrite([3(2),1690(5),8(6,R),4(5),1160(6),1547(3),871(4)])].
% 1.97/2.27 1726 meet(join(A,B),join(B,join(C,meet(B,join(A,C))))) = join(B,meet(A,join(B,C))). [back_rewrite(867),rewrite([1690(4),8(5,R),4(4),18(6)])].
% 1.97/2.27 1729 join(meet(A,B),meet(C,join(meet(A,B),meet(A,C)))) = meet(A,join(C,meet(A,B))). [back_rewrite(1713),rewrite([3(1),1724(6),1406(5),3(4),3(5)]),flip(a)].
% 1.97/2.27 1731 join(meet(A,B),meet(C,join(meet(A,B),meet(C,join(A,B))))) = meet(join(A,B),join(C,meet(A,B))). [back_rewrite(908),rewrite([1724(12)])].
% 1.97/2.27 1911 join(A,join(B,meet(B,join(A,C)))) = join(A,join(B,meet(A,C))). [para(50(a,1),1209(a,2,2,2)),rewrite([8(7,R),4(6),18(8)])].
% 1.97/2.27 1919 join(A,join(B,meet(A,meet(C,D)))) = join(A,join(B,meet(A,join(C,D)))). [para(72(a,2),1209(a,2,2,2)),rewrite([1547(4),8(2,R),4(1),1911(5),1174(9)]),flip(a)].
% 1.97/2.27 1989 meet(join(A,B),join(C,meet(A,join(B,meet(A,meet(B,C)))))) = join(meet(B,join(A,C)),meet(C,join(A,B))). [back_rewrite(1399),rewrite([1911(4),1426(9)])].
% 1.97/2.27 1995 join(join(A,B),meet(C,join(A,meet(A,D)))) = join(A,join(B,meet(A,join(C,D)))). [back_rewrite(1542),rewrite([1919(9)])].
% 1.97/2.27 2095 join(A,join(B,meet(A,join(C,B)))) = join(A,join(B,meet(A,C))). [para(1361(a,1),156(a,1,2,2)),rewrite([4(2),3(3),1995(6),8(6,R),4(5),8(5,R),4(4),10(4),4(6),8(7),4(6),8(7,R),4(6)])].
% 1.97/2.27 2101 meet(A,meet(join(B,meet(C,D)),join(meet(C,D),meet(C,B)))) = meet(A,join(meet(C,D),meet(C,B))). [para(207(a,1),1361(a,1,2)),rewrite([3(2),3(4),3(7),6(7,R),3(6),3(9),3(12),530(15),3(11),6(11),3(10),6(11,R),3(10),1031(13)])].
% 1.97/2.27 2120 meet(join(A,B),join(B,C)) = join(B,meet(A,join(B,C))). [back_rewrite(1726),rewrite([2095(5),3(2),1010(5)])].
% 1.97/2.27 2136 meet(A,join(meet(B,C),meet(D,join(meet(B,C),meet(D,B))))) = meet(A,join(meet(B,C),meet(D,B))). [back_rewrite(2101),rewrite([3(4),2120(6),3(9)])].
% 1.97/2.27 2173 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [back_rewrite(27),rewrite([2120(4)])].
% 1.97/2.27 2365 meet(A,meet(B,join(C,meet(B,D)))) = meet(A,join(meet(B,D),meet(B,C))). [back_rewrite(2136),rewrite([3(3),1729(6),3(6)])].
% 1.97/2.27 2366 meet(join(A,B),join(C,meet(A,B))) = join(meet(A,B),meet(C,join(A,B))). [back_rewrite(1731),rewrite([2173(7)]),flip(a)].
% 1.97/2.27 2387 meet(A,join(meet(A,B),meet(C,join(A,B)))) = meet(A,join(C,meet(A,B))). [back_rewrite(380),rewrite([2366(4)])].
% 1.97/2.27 2535 meet(A,join(B,meet(C,join(B,A)))) = meet(A,join(C,B)). [para(1364(a,1),1128(a,2)),rewrite([3(2),4(3),3(4),6(4,R),2120(3)])].
% 1.97/2.27 2564 meet(A,join(meet(B,C),meet(A,B))) = meet(A,join(B,meet(B,C))). [para(72(a,1),1461(a,1,2)),rewrite([3(4),2366(4),2387(5),2365(4),3(2)])].
% 1.97/2.27 2607 join(meet(A,B),meet(C,join(A,meet(A,B)))) = join(meet(A,B),meet(A,C)). [para(17(a,1),44(a,1,2,2,2,2)),rewrite([662(4),139(8),6(7,R),3(6),8(9),4(8),21(8),23(7),17(9),139(10),6(9,R),3(8),1031(11)])].
% 1.97/2.27 2943 meet(A,join(B,meet(A,C))) = join(meet(A,C),meet(B,A)). [para(67(a,1),28(a,1,2)),rewrite([2(3),2365(6),3(4),2120(6),2564(5),2607(5),3(2),67(8)]),flip(a)].
% 1.97/2.27 3032 meet(A,join(meet(A,B),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)). [back_rewrite(2387),rewrite([2943(8),3(7)])].
% 1.97/2.27 3043 join(meet(A,join(B,C)),meet(C,join(B,A))) = join(meet(B,A),meet(C,join(B,A))). [back_rewrite(1989),rewrite([2943(5),3(4),4(5),668(5),1724(5),2366(4)]),flip(a)].
% 1.97/2.27 4107 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [para(2535(a,1),2535(a,2)),rewrite([4(1),4(3),4(5),2535(6),4(3),3043(5),3032(5)])].
% 1.97/2.27 4108 $F # answer(prove_distributivity). [resolve(4107,a,16,a)].
% 1.97/2.27
% 1.97/2.27 % SZS output end Refutation
% 1.97/2.27 ============================== end of proof ==========================
% 1.97/2.27
% 1.97/2.27 ============================== STATISTICS ============================
% 1.97/2.27
% 1.97/2.27 Given=97. Generated=18542. Kept=4101. proofs=1.
% 1.97/2.27 Usable=60. Sos=1614. Demods=1627. Limbo=37, Disabled=2399. Hints=0.
% 1.97/2.27 Megabytes=5.30.
% 1.97/2.27 User_CPU=1.30, System_CPU=0.01, Wall_clock=1.
% 1.97/2.27
% 1.97/2.27 ============================== end of statistics =====================
% 1.97/2.27
% 1.97/2.27 ============================== end of search =========================
% 1.97/2.27
% 1.97/2.27 THEOREM PROVED
% 1.97/2.27 % SZS status Unsatisfiable
% 1.97/2.27
% 1.97/2.27 Exiting with 1 proof.
% 1.97/2.27
% 1.97/2.27 Process 22164 exit (max_proofs) Thu Jun 30 13:26:40 2022
% 1.97/2.27 Prover9 interrupted
%------------------------------------------------------------------------------