TSTP Solution File: LAT144-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT144-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n021.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 07:15:21 EDT 2022
% Result : Unsatisfiable 58.53s 58.92s
% Output : CNFRefutation 58.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT144-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 23:48:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.95 ********************************************************************************
% 0.54/0.95 * W A L D M E I S T E R \| \ / \|/ *
% 0.54/0.95 * |/ | \/ | *
% 0.54/0.95 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.54/0.95 * A. Jaeger and B. Loechner | | *
% 0.54/0.95 * <waldmeister@informatik.uni-kl.de> | *
% 0.54/0.95 ********************************************************************************
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Goals:
% 0.54/0.95 ------
% 0.54/0.95
% 0.54/0.95 ( 1) meet(a,join(b,meet(a,c))) ?=? meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c)))))
% 0.54/0.95
% 0.54/0.95 Detected structure: Verband
% 0.54/0.95 ********************************************************************************
% 0.54/0.95 ****************************** COMPLETION - PROOF ******************************
% 0.54/0.95 ********************************************************************************
% 0.54/0.95
% 58.53/58.92 joined goal: 1 meet(a,join(b,meet(a,c))) ?= meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) to meet(a,join(b,meet(c,a)))
% 58.53/58.92 goal joined
% 58.53/58.92 % SZS status Unsatisfiable
% 58.53/58.92 #START OF PROOF
% 58.53/58.92 % SZS output start CNFRefutation
% 58.53/58.92 cnf('0.1.0.0',axiom,
% 58.53/58.92 ( X1 = meet(X1,X1) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.1.1.0',plain,
% 58.53/58.92 ( X1 = meet(X1,X1) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.1.0.0']),
% 58.53/58.92 [weight('<0,0,0,[0,0,0,1]>')]).
% 58.53/58.92 cnf('0.1.2.0',plain,
% 58.53/58.92 ( meet(X1,X1) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_1]).
% 58.53/58.92 cnf('0.2.0.0',axiom,
% 58.53/58.92 ( X1 = meet(X1,join(X1,X2)) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.2.1.0',plain,
% 58.53/58.92 ( X1 = meet(X1,join(X1,X2)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.2.0.0']),
% 58.53/58.92 [weight('<1,0,0,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.2.2.0',plain,
% 58.53/58.92 ( meet(X1,join(X1,X2)) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_2]).
% 58.53/58.92 cnf('0.3.0.0',axiom,
% 58.53/58.92 ( X1 = join(X1,X1) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.3.1.0',plain,
% 58.53/58.92 ( X1 = join(X1,X1) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.3.0.0']),
% 58.53/58.92 [weight('<2,0,0,[0,0,0,3]>')]).
% 58.53/58.92 cnf('0.3.2.0',plain,
% 58.53/58.92 ( join(X1,X1) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_3]).
% 58.53/58.92 cnf('0.4.0.0',axiom,
% 58.53/58.92 ( X1 = join(X1,meet(X1,X2)) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.4.1.0',plain,
% 58.53/58.92 ( X1 = join(X1,meet(X1,X2)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.4.0.0']),
% 58.53/58.92 [weight('<3,0,0,[0,0,0,4]>')]).
% 58.53/58.92 cnf('0.4.2.0',plain,
% 58.53/58.92 ( join(X1,meet(X1,X2)) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_4]).
% 58.53/58.92 cnf('0.5.0.0',axiom,
% 58.53/58.92 ( meet(X1,X2) = meet(X2,X1) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.5.1.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X2,X1) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.5.0.0']),
% 58.53/58.92 [weight('<4,0,0,[0,0,0,5]>')]).
% 58.53/58.92 cnf('0.5.2.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X2,X1) ),
% 58.53/58.92 inference(activate,[status(thm)],['0.5.1.0']),
% 58.53/58.92 [equation_1]).
% 58.53/58.92 cnf('0.6.0.0',axiom,
% 58.53/58.92 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.6.1.0',plain,
% 58.53/58.92 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.6.0.0']),
% 58.53/58.92 [weight('<5,0,0,[0,0,0,6]>')]).
% 58.53/58.92 cnf('0.6.2.0',plain,
% 58.53/58.92 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_5]).
% 58.53/58.92 cnf('0.7.0.0',axiom,
% 58.53/58.92 ( meet(X1,join(X2,meet(X1,meet(X3,X4)))) = meet(X1,join(X2,meet(X3,join(meet(X1,X4),meet(X2,X4))))) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.7.1.0',plain,
% 58.53/58.92 ( meet(X1,join(X2,meet(X1,meet(X3,X4)))) = meet(X1,join(X2,meet(X3,join(meet(X1,X4),meet(X2,X4))))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.7.0.0']),
% 58.53/58.92 [weight('<6,0,0,[0,0,0,7]>')]).
% 58.53/58.92 cnf('0.7.2.0',plain,
% 58.53/58.92 ( meet(X1,join(X2,meet(X3,join(meet(X1,X4),meet(X2,X4))))) = meet(X1,join(X2,meet(X1,meet(X3,X4)))) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_6]).
% 58.53/58.92 cnf('0.8.0.0',axiom,
% 58.53/58.92 ( join(X1,X2) = join(X2,X1) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.8.1.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X2,X1) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.8.0.0']),
% 58.53/58.92 [weight('<7,0,0,[0,0,0,8]>')]).
% 58.53/58.92 cnf('0.8.2.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X2,X1) ),
% 58.53/58.92 inference(activate,[status(thm)],['0.8.1.0']),
% 58.53/58.92 [equation_2]).
% 58.53/58.92 cnf('0.9.0.0',axiom,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 58.53/58.92 file('/tmp/WALDMEISTER_31655_n021')).
% 58.53/58.92 cnf('0.9.1.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.9.0.0']),
% 58.53/58.92 [weight('<8,0,0,[0,0,0,9]>')]).
% 58.53/58.92 cnf('0.9.2.0',plain,
% 58.53/58.92 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_7]).
% 58.53/58.92 cnf('0.10.0.0',plain,
% 58.53/58.92 ( X1 = join(X1,meet(X2,X1)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.10.1.0',plain,
% 58.53/58.92 ( X1 = join(X1,meet(X2,X1)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.10.0.0']),
% 58.53/58.92 [weight('<5,5,4,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.10.2.0',plain,
% 58.53/58.92 ( join(X1,meet(X2,X1)) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_8]).
% 58.53/58.92 cnf('0.11.0.0',plain,
% 58.53/58.92 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.6.2.0','0.1.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.11.1.0',plain,
% 58.53/58.92 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.11.0.0']),
% 58.53/58.92 [weight('<5,6,1,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.11.2.0',plain,
% 58.53/58.92 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_9]).
% 58.53/58.92 cnf('0.12.0.0',plain,
% 58.53/58.92 ( X1 = meet(X1,join(X2,X1)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.2.2.0','0.8.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.12.1.0',plain,
% 58.53/58.92 ( X1 = meet(X1,join(X2,X1)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.12.0.0']),
% 58.53/58.92 [weight('<5,8,2,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.12.2.0',plain,
% 58.53/58.92 ( meet(X1,join(X2,X1)) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_10]).
% 58.53/58.92 cnf('0.13.0.0',plain,
% 58.53/58.92 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.9.2.0','0.3.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.13.1.0',plain,
% 58.53/58.92 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.13.0.0']),
% 58.53/58.92 [weight('<5,9,3,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.13.2.0',plain,
% 58.53/58.92 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_11]).
% 58.53/58.92 cnf('0.14.0.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(join(X1,X2),X1) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.10.2.0','0.2.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.14.0.1',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.14.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.14.1.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.14.0.1']),
% 58.53/58.92 [weight('<5,10,2,[1,0,0,2]>')]).
% 58.53/58.92 cnf('0.14.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_12]).
% 58.53/58.92 cnf('0.16.0.0',plain,
% 58.53/58.92 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.16.1.0',plain,
% 58.53/58.92 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.16.0.0']),
% 58.53/58.92 [weight('<7,6,2,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.16.2.0',plain,
% 58.53/58.92 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_14]).
% 58.53/58.92 cnf('0.17.0.0',plain,
% 58.53/58.92 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.17.1.0',plain,
% 58.53/58.92 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.17.0.0']),
% 58.53/58.92 [weight('<7,9,4,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.17.2.0',plain,
% 58.53/58.92 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_15]).
% 58.53/58.92 cnf('0.18.0.0',plain,
% 58.53/58.92 ( X1 = join(X1,meet(X2,meet(X3,X1))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.10.2.0','0.6.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.18.1.0',plain,
% 58.53/58.92 ( X1 = join(X1,meet(X2,meet(X3,X1))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.18.0.0']),
% 58.53/58.92 [weight('<7,10,6,[1,0,0,2]>')]).
% 58.53/58.92 cnf('0.18.2.0',plain,
% 58.53/58.92 ( join(X1,meet(X2,meet(X3,X1))) = X1 ),
% 58.53/58.92 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_16]).
% 58.53/58.92 cnf('0.20.0.0',plain,
% 58.53/58.92 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.6.2.0','0.12.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.20.1.0',plain,
% 58.53/58.92 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.20.0.0']),
% 58.53/58.92 [weight('<7,12,6,[0,0,0,1]>')]).
% 58.53/58.92 cnf('0.20.2.0',plain,
% 58.53/58.92 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_18]).
% 58.53/58.92 cnf('0.22.0.0',plain,
% 58.53/58.92 ( join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.9.2.0','0.14.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.22.0.1',plain,
% 58.53/58.92 ( join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.22.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.22.0.2',plain,
% 58.53/58.92 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.22.0.1','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.22.1.0',plain,
% 58.53/58.92 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.22.0.2']),
% 58.53/58.92 [weight('<7,14,9,[0,0,0,1]>')]).
% 58.53/58.92 cnf('0.22.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_20]).
% 58.53/58.92 cnf('0.28.0.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X3))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.16.2.0','0.5.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.28.1.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X3))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.28.0.0']),
% 58.53/58.92 [weight('<7,16,5,[1,0,0,2]>')]).
% 58.53/58.92 cnf('0.28.2.0',plain,
% 58.53/58.92 ( meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_26]).
% 58.53/58.92 cnf('0.30.0.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,meet(X1,X3))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.17.2.0','0.8.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.30.1.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,meet(X1,X3))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.30.0.0']),
% 58.53/58.92 [weight('<7,17,8,[1,0,0,2]>')]).
% 58.53/58.92 cnf('0.30.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,meet(X1,X3))) = join(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_28]).
% 58.53/58.92 cnf('0.32.0.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(join(X1,X2),meet(X3,X1)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.18.2.0','0.2.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2.2','L')]).
% 58.53/58.92 cnf('0.32.0.1',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,meet(X3,X1))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.32.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.32.1.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,meet(X3,X1))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.32.0.1']),
% 58.53/58.92 [weight('<7,18,2,[1,0,0,4]>')]).
% 58.53/58.92 cnf('0.32.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,meet(X3,X1))) = join(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_30]).
% 58.53/58.92 cnf('0.37.0.0',plain,
% 58.53/58.92 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 58.53/58.92 [pos('L','L')]).
% 58.53/58.92 cnf('0.37.1.0',plain,
% 58.53/58.92 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.37.0.0']),
% 58.53/58.92 [weight('<9,9,4,[1,0,0,0]>')]).
% 58.53/58.92 cnf('0.37.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_35]).
% 58.53/58.92 cnf('0.38.0.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.10.2.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('L','L')]).
% 58.53/58.92 cnf('0.38.1.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.38.0.0']),
% 58.53/58.92 [weight('<9,10,9,[1,0,0,0]>')]).
% 58.53/58.92 cnf('0.38.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_36]).
% 58.53/58.92 cnf('0.39.0.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 58.53/58.92 [pos('L','L')]).
% 58.53/58.92 cnf('0.39.1.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.39.0.0']),
% 58.53/58.92 [weight('<9,12,6,[1,0,0,0]>')]).
% 58.53/58.92 cnf('0.39.2.0',plain,
% 58.53/58.92 ( meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_37]).
% 58.53/58.92 cnf('0.40.0.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.10.2.0','0.16.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.40.1.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.40.0.0']),
% 58.53/58.92 [weight('<9,16,10,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.40.1.1',plain,
% 58.53/58.92 ( meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.40.1.0','0.8.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.40.2.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.40.1.1',theory(equality)]),
% 58.53/58.92 [x,rule_38]).
% 58.53/58.92 cnf('0.41.0.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),meet(X1,X3)) = join(meet(X1,X3),meet(join(X1,X2),meet(X1,X3))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.40.2.0','0.11.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.41.0.1',plain,
% 58.53/58.92 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.41.0.0','0.10.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.41.1.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.41.0.1']),
% 58.53/58.92 [weight('<7,40,11,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.41.2.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_39]).
% 58.53/58.92 cnf('0.43.0.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(join(X3,X1),meet(X1,X2)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.41.2.0','0.8.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.43.1.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(join(X3,X1),meet(X1,X2)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.43.0.0']),
% 58.53/58.92 [weight('<7,41,8,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.43.2.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),meet(X2,X3)) = meet(X2,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_41]).
% 58.53/58.92 cnf('0.45.0.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.12.2.0','0.17.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.45.1.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.45.0.0']),
% 58.53/58.92 [weight('<9,17,12,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.45.1.1',plain,
% 58.53/58.92 ( join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.45.1.0','0.5.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.45.2.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.45.1.1',theory(equality)]),
% 58.53/58.92 [x,rule_43]).
% 58.53/58.92 cnf('0.46.0.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),join(X1,X3)) = meet(join(X1,X3),join(meet(X1,X2),join(X1,X3))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.45.2.0','0.13.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.46.0.1',plain,
% 58.53/58.92 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.46.0.0','0.12.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.46.1.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.46.0.1']),
% 58.53/58.92 [weight('<7,45,13,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.46.2.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 58.53/58.92 [u,rule_44]).
% 58.53/58.92 cnf('0.48.0.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(meet(X1,X3),join(X2,X1)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.46.2.0','0.8.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.48.1.0',plain,
% 58.53/58.92 ( join(X1,X2) = join(meet(X1,X3),join(X2,X1)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.48.0.0']),
% 58.53/58.92 [weight('<7,46,8,[1,0,0,4]>')]).
% 58.53/58.92 cnf('0.48.2.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),join(X3,X1)) = join(X1,X3) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_46]).
% 58.53/58.92 cnf('0.58.0.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.10.2.0','0.20.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.58.1.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.58.0.0']),
% 58.53/58.92 [weight('<9,20,10,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.58.1.1',plain,
% 58.53/58.92 ( meet(join(X1,X2),X3) = join(meet(X2,X3),meet(join(X1,X2),X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.58.1.0','0.8.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.58.2.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.58.1.1',theory(equality)]),
% 58.53/58.92 [x,rule_56]).
% 58.53/58.92 cnf('0.84.0.0',plain,
% 58.53/58.92 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X2,X1)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.12.2.0','0.30.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.84.1.0',plain,
% 58.53/58.92 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X2,X1)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.84.0.0']),
% 58.53/58.92 [weight('<9,30,12,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.84.1.1',plain,
% 58.53/58.92 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,meet(X2,X3))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.84.1.0','0.5.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.84.2.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.84.1.1',theory(equality)]),
% 58.53/58.92 [x,rule_82]).
% 58.53/58.92 cnf('0.86.0.0',plain,
% 58.53/58.92 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X3,X1)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.12.2.0','0.32.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2','L')]).
% 58.53/58.92 cnf('0.86.1.0',plain,
% 58.53/58.92 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X3,X1)) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.86.0.0']),
% 58.53/58.92 [weight('<9,32,12,[0,0,0,2]>')]).
% 58.53/58.92 cnf('0.86.1.1',plain,
% 58.53/58.92 ( join(X1,meet(X2,X3)) = meet(join(X3,X1),join(X1,meet(X2,X3))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.86.1.0','0.5.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.86.2.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(X2,meet(X3,X1))) = join(X2,meet(X3,X1)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.86.1.1',theory(equality)]),
% 58.53/58.92 [x,rule_84]).
% 58.53/58.92 cnf('0.95.0.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.39.2.0','0.5.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.2.2.2','L')]).
% 58.53/58.92 cnf('0.95.1.0',plain,
% 58.53/58.92 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.95.0.0']),
% 58.53/58.92 [weight('<9,39,5,[1,0,0,6]>')]).
% 58.53/58.92 cnf('0.95.2.0',plain,
% 58.53/58.92 ( meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_93]).
% 58.53/58.92 cnf('0.106.0.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.45.2.0','0.4.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.106.1.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.106.0.0']),
% 58.53/58.92 [weight('<9,45,4,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.106.2.0',plain,
% 58.53/58.92 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_104]).
% 58.53/58.92 cnf('0.109.0.0',plain,
% 58.53/58.92 ( join(join(X1,X2),X3) = join(meet(X2,X4),join(join(X1,X2),X3)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.46.2.0','0.43.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.109.0.1',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X2,X4),join(join(X1,X2),X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.109.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('L','L')]).
% 58.53/58.92 cnf('0.109.0.2',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X2,X4),join(X1,join(X2,X3))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.109.0.1','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('R.2','L')]).
% 58.53/58.92 cnf('0.109.1.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X2,X4),join(X1,join(X2,X3))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.109.0.2']),
% 58.53/58.92 [weight('<9,46,43,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.109.2.0',plain,
% 58.53/58.92 ( join(meet(X1,X2),join(X3,join(X1,X4))) = join(X3,join(X1,X4)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_107]).
% 58.53/58.92 cnf('0.110.0.0',plain,
% 58.53/58.92 ( join(join(X1,X2),X3) = join(join(meet(X1,X4),X2),join(join(X1,X2),X3)) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.46.2.0','0.45.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.110.0.1',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(join(meet(X1,X4),X2),join(join(X1,X2),X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.110.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('L','L')]).
% 58.53/58.92 cnf('0.110.0.2',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X2,join(join(X1,X2),X3))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.110.0.1','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.110.0.3',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X2,join(X1,join(X2,X3)))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.110.0.2','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('R.2.2','L')]).
% 58.53/58.92 cnf('0.110.0.4',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X2,join(X1,X3))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.110.0.3','0.22.2.0',theory(equality)]),
% 58.53/58.92 [pos('R.2','L')]).
% 58.53/58.92 cnf('0.110.1.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X2,join(X1,X3))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.110.0.4']),
% 58.53/58.92 [weight('<9,46,45,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.110.1.1',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(X2,join(X1,X3)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.110.1.0','0.109.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.110.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(X2,join(X1,X3)) ),
% 58.53/58.92 inference(activate,[status(thm)],['0.110.1.1']),
% 58.53/58.92 [equation_3]).
% 58.53/58.92 cnf('0.112.0.0',plain,
% 58.53/58.92 ( join(join(X1,X2),X3) = join(meet(X1,X4),join(X3,join(X1,X2))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.48.2.0','0.41.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.112.0.1',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X3,join(X1,X2))) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.112.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.92 [pos('L','L')]).
% 58.53/58.92 cnf('0.112.1.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X3,join(X1,X2))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.112.0.1']),
% 58.53/58.92 [weight('<9,48,41,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.112.1.1',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 58.53/58.92 inference(reduction,[status(thm)],['0.112.1.0','0.109.2.0',theory(equality)]),
% 58.53/58.92 [pos('R','L')]).
% 58.53/58.92 cnf('0.112.2.0',plain,
% 58.53/58.92 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 58.53/58.92 inference(activate,[status(thm)],['0.112.1.1']),
% 58.53/58.92 [equation_4]).
% 58.53/58.92 cnf('0.116.0.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),join(X2,X3))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.58.2.0','0.2.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.116.1.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),join(X2,X3))) ),
% 58.53/58.92 inference(weigh,[status(thm)],['0.116.0.0']),
% 58.53/58.92 [weight('<9,58,2,[1,0,0,1]>')]).
% 58.53/58.92 cnf('0.116.2.0',plain,
% 58.53/58.92 ( join(X1,meet(join(X2,X1),join(X1,X3))) = meet(join(X2,X1),join(X1,X3)) ),
% 58.53/58.92 inference(orient,[status(thm)],['0.116.1.0',theory(equality)]),
% 58.53/58.92 [x,rule_112]).
% 58.53/58.92 cnf('0.118.0.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(X3,X2)) = join(X2,meet(join(X1,X2),join(X3,X2))) ),
% 58.53/58.92 inference(cp,[status(thm)],['0.58.2.0','0.12.2.0',theory(equality)]),
% 58.53/58.92 [pos('L.1','L')]).
% 58.53/58.92 cnf('0.118.1.0',plain,
% 58.53/58.92 ( meet(join(X1,X2),join(X3,X2)) = join(X2,meet(join(X1,X2),join(X3,X2))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.118.0.0']),
% 58.53/58.93 [weight('<9,58,12,[1,0,0,1]>')]).
% 58.53/58.93 cnf('0.118.2.0',plain,
% 58.53/58.93 ( join(X1,meet(join(X2,X1),join(X3,X1))) = meet(join(X2,X1),join(X3,X1)) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.118.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_114]).
% 58.53/58.93 cnf('0.128.0.0',plain,
% 58.53/58.93 ( meet(X1,X2) = meet(X1,join(meet(X2,X3),meet(X2,X1))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.95.2.0','0.106.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.128.1.0',plain,
% 58.53/58.93 ( meet(X1,X2) = meet(X1,join(meet(X2,X3),meet(X2,X1))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.128.0.0']),
% 58.53/58.93 [weight('<9,106,95,[0,0,0,2]>')]).
% 58.53/58.93 cnf('0.128.2.0',plain,
% 58.53/58.93 ( meet(X1,join(meet(X2,X3),meet(X2,X1))) = meet(X1,X2) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.128.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_123]).
% 58.53/58.93 cnf('0.136.0.0',plain,
% 58.53/58.93 ( join(X1,X2) = join(X1,meet(join(X1,X2),join(X2,X3))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.37.2.0','0.116.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.136.1.0',plain,
% 58.53/58.93 ( join(X1,X2) = join(X1,meet(join(X1,X2),join(X2,X3))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.136.0.0']),
% 58.53/58.93 [weight('<9,116,37,[0,0,0,2]>')]).
% 58.53/58.93 cnf('0.136.2.0',plain,
% 58.53/58.93 ( join(X1,meet(join(X1,X2),join(X2,X3))) = join(X1,X2) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.136.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_130]).
% 58.53/58.93 cnf('0.139.0.0',plain,
% 58.53/58.93 ( join(X1,X2) = join(X1,meet(join(X3,X2),join(X1,X2))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.38.2.0','0.118.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.139.1.0',plain,
% 58.53/58.93 ( join(X1,X2) = join(X1,meet(join(X3,X2),join(X1,X2))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.139.0.0']),
% 58.53/58.93 [weight('<9,118,38,[0,0,0,2]>')]).
% 58.53/58.93 cnf('0.139.2.0',plain,
% 58.53/58.93 ( join(X1,meet(join(X2,X3),join(X1,X3))) = join(X1,X3) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_133]).
% 58.53/58.93 cnf('0.150.0.0',plain,
% 58.53/58.93 ( join(X1,meet(X2,X3)) = join(X1,meet(join(X1,meet(X2,X3)),X2)) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.136.2.0','0.128.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.150.1.0',plain,
% 58.53/58.93 ( join(X1,meet(X2,X3)) = join(X1,meet(join(X1,meet(X2,X3)),X2)) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.150.0.0']),
% 58.53/58.93 [weight('<9,136,128,[1,0,0,2]>')]).
% 58.53/58.93 cnf('0.150.1.1',plain,
% 58.53/58.93 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,join(X1,meet(X2,X3)))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.150.1.0','0.5.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2','L')]).
% 58.53/58.93 cnf('0.150.2.0',plain,
% 58.53/58.93 ( join(X1,meet(X2,join(X1,meet(X2,X3)))) = join(X1,meet(X2,X3)) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.150.1.1',theory(equality)]),
% 58.53/58.93 [x,rule_144]).
% 58.53/58.93 cnf('0.731.0.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,meet(X3,join(X1,X4))))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,join(X1,X4)))))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2.2.1','L')]).
% 58.53/58.93 cnf('0.731.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,meet(X3,join(X1,X4))))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,join(X1,X4)))))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.731.0.0']),
% 58.53/58.93 [weight('<13,7,2,[1,0,0,7]>')]).
% 58.53/58.93 cnf('0.731.1.1',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,join(X1,X4)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.731.1.0','0.28.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2','L')]).
% 58.53/58.93 cnf('0.731.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X1,meet(X2,join(X1,X4)))))) = meet(X1,join(X2,meet(X1,X3))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.731.1.1',theory(equality)]),
% 58.53/58.93 [x,rule_723]).
% 58.53/58.93 cnf('0.732.0.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.731.2.0','0.12.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2.2.2','L')]).
% 58.53/58.93 cnf('0.732.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.732.0.0']),
% 58.53/58.93 [weight('<9,731,12,[1,0,0,8]>')]).
% 58.53/58.93 cnf('0.732.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.732.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_724]).
% 58.53/58.93 cnf('0.734.0.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.732.2.0','0.8.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2.2','L')]).
% 58.53/58.93 cnf('0.734.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.734.0.0']),
% 58.53/58.93 [weight('<9,732,8,[1,0,0,6]>')]).
% 58.53/58.93 cnf('0.734.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X1,X3))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.734.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_726]).
% 58.53/58.93 cnf('0.736.0.0',plain,
% 58.53/58.93 ( meet(X1,join(join(X2,X3),meet(X1,X4))) = meet(X1,join(join(X2,X3),meet(X4,join(X1,X3)))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.731.2.0','0.139.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2.2','L')]).
% 58.53/58.93 cnf('0.736.0.1',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(join(X2,X3),meet(X4,join(X1,X3)))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.736.0.0','0.9.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.736.0.2',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(X2,join(X3,meet(X4,join(X1,X3))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.736.0.1','0.9.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2','L')]).
% 58.53/58.93 cnf('0.736.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(X2,join(X3,meet(X4,join(X1,X3))))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.736.0.2']),
% 58.53/58.93 [weight('<11,731,139,[1,0,0,6]>')]).
% 58.53/58.93 cnf('0.736.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X3))))) = meet(X1,join(X2,join(X3,meet(X1,X4)))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.736.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_728]).
% 58.53/58.93 cnf('0.753.0.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X2,join(X4,X1))))) = meet(X1,meet(join(X4,X1),join(X2,meet(join(X4,X1),X3)))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.20.2.0','0.734.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.753.0.1',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X2,join(X4,X1))))) = meet(X1,join(X2,meet(join(X4,X1),X3))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.753.0.0','0.20.2.0',theory(equality)]),
% 58.53/58.93 [pos('R','L')]).
% 58.53/58.93 cnf('0.753.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X2,join(X4,X1))))) = meet(X1,join(X2,meet(join(X4,X1),X3))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.753.0.1']),
% 58.53/58.93 [weight('<11,734,20,[0,0,0,2]>')]).
% 58.53/58.93 cnf('0.753.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X2,join(X4,X1))))) = meet(X1,join(X2,meet(join(X4,X1),X3))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.753.1.0',theory(equality)]),
% 58.53/58.93 [u,rule_745]).
% 58.53/58.93 cnf('0.766.0.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(X3,join(X2,meet(X4,join(X1,X3))))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.736.2.0','0.110.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.766.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(X3,join(X2,meet(X4,join(X1,X3))))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.766.0.0']),
% 58.53/58.93 [weight('<11,736,110,[1,0,0,2]>')]).
% 58.53/58.93 cnf('0.766.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(X3,join(X2,meet(X1,X4)))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.766.1.0',theory(equality)]),
% 58.53/58.93 [x,rule_758]).
% 58.53/58.93 cnf('0.3753.0.0',plain,
% 58.53/58.93 ( meet(meet(X1,join(X2,X3)),join(X3,meet(join(X4,meet(X1,join(X2,X3))),X2))) = meet(meet(X1,join(X2,X3)),join(X3,meet(X2,join(X4,join(X3,meet(X2,X1)))))) ),
% 58.53/58.93 inference(cp,[status(thm)],['0.753.2.0','0.766.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2','L')]).
% 58.53/58.93 cnf('0.3753.0.1',plain,
% 58.53/58.93 ( meet(X1,meet(join(X2,X3),join(X3,meet(join(X4,meet(X1,join(X2,X3))),X2)))) = meet(meet(X1,join(X2,X3)),join(X3,meet(X2,join(X4,join(X3,meet(X2,X1)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.3753.0.0','0.6.2.0',theory(equality)]),
% 58.53/58.93 [pos('L','L')]).
% 58.53/58.93 cnf('0.3753.0.2',plain,
% 58.53/58.93 ( meet(X1,join(X3,meet(join(X4,meet(X1,join(X2,X3))),X2))) = meet(meet(X1,join(X2,X3)),join(X3,meet(X2,join(X4,join(X3,meet(X2,X1)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.3753.0.1','0.86.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2','L')]).
% 58.53/58.93 cnf('0.3753.0.3',plain,
% 58.53/58.93 ( meet(X1,join(X3,meet(join(X4,meet(X1,join(X2,X3))),X2))) = meet(X1,meet(join(X2,X3),join(X3,meet(X2,join(X4,join(X3,meet(X2,X1))))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.3753.0.2','0.6.2.0',theory(equality)]),
% 58.53/58.93 [pos('R','L')]).
% 58.53/58.93 cnf('0.3753.0.4',plain,
% 58.53/58.93 ( meet(X1,join(X3,meet(join(X4,meet(X1,join(X2,X3))),X2))) = meet(X1,join(X3,meet(X2,join(X4,join(X3,meet(X2,X1)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.3753.0.3','0.84.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2','L')]).
% 58.53/58.93 cnf('0.3753.1.0',plain,
% 58.53/58.93 ( meet(X1,join(X3,meet(join(X4,meet(X1,join(X2,X3))),X2))) = meet(X1,join(X3,meet(X2,join(X4,join(X3,meet(X2,X1)))))) ),
% 58.53/58.93 inference(weigh,[status(thm)],['0.3753.0.4']),
% 58.53/58.93 [weight('<13,766,753,[0,0,0,4]>')]).
% 58.53/58.93 cnf('0.3753.1.1',plain,
% 58.53/58.93 ( meet(X1,join(X3,meet(X2,join(X4,meet(X1,join(X2,X3)))))) = meet(X1,join(X3,meet(X2,join(X4,join(X3,meet(X2,X1)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['0.3753.1.0','0.5.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2','L')]).
% 58.53/58.93 cnf('0.3753.2.0',plain,
% 58.53/58.93 ( meet(X1,join(X2,meet(X3,join(X4,meet(X1,join(X3,X2)))))) = meet(X1,join(X2,meet(X3,join(X4,join(X2,meet(X3,X1)))))) ),
% 58.53/58.93 inference(orient,[status(thm)],['0.3753.1.1',theory(equality)]),
% 58.53/58.93 [u,rule_3743]).
% 58.53/58.93 cnf('1.0.0.0',conjecture,
% 58.53/58.93 ( meet(a,join(b,meet(a,c))) = meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) ),
% 58.53/58.93 file('/tmp/WALDMEISTER_31655_n021',conjecture_1)).
% 58.53/58.93 cnf('1.0.0.1',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.0','0.5.2.0',theory(equality)]),
% 58.53/58.93 [pos('L.2.2','L')]).
% 58.53/58.93 cnf('1.0.0.2',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(meet(b,c),meet(a,join(b,c)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.1','0.8.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2.2.2','L')]).
% 58.53/58.93 cnf('1.0.0.3',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(meet(c,b),meet(a,join(b,c)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.2','0.5.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2.2.2.1','L')]).
% 58.53/58.93 cnf('1.0.0.4',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(meet(c,b),meet(a,join(c,b)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.3','0.8.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2.2.2.2.2','L')]).
% 58.53/58.93 cnf('1.0.0.5',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(meet(c,b),join(b,meet(c,a)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.4','0.3753.2.0',theory(equality)]),
% 58.53/58.93 [pos('R','L')]).
% 58.53/58.93 cnf('1.0.0.6',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(b,join(meet(c,a),meet(c,b)))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.5','0.112.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2.2.2','R')]).
% 58.53/58.93 cnf('1.0.0.7',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(b,meet(c,a))))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.6','0.32.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2.2.2','L')]).
% 58.53/58.93 cnf('1.0.0.8',plain,
% 58.53/58.93 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,a))) ),
% 58.53/58.93 inference(reduction,[status(thm)],['1.0.0.7','0.150.2.0',theory(equality)]),
% 58.53/58.93 [pos('R.2','L')]).
% 58.53/58.93 cnf('1.0.0.9',plain,
% 58.53/58.93 ( $true ),
% 58.53/58.93 inference(trivial,[status(thm)],['1.0.0.8',theory(equality)]),
% 58.53/58.93 [conjecture_1]).
% 58.53/58.93
% 58.53/58.93 Proved Goals:
% 58.53/58.93 No. 1: meet(a,join(b,meet(a,c))) ?= meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) joined, current: meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,a)))
% 58.53/58.93 1 goal was specified, which was proved.
% 58.53/58.93 % SZS output end CNFRefutation
% 58.53/58.93 #END OF PROOF
% 58.53/58.93
% 58.53/58.93 Problem WALDMEISTER_31655_n021
% 58.53/58.93 CPs.gen 14399903
% 58.53/58.93 CPs.reexp 0
% 58.53/58.93 Select 266187
% 58.53/58.93 R 3743
% 58.53/58.93 E 10
% 58.53/58.93 vsize 11.3M
% 58.53/58.93 rss 6.7M
% 58.53/58.93 process.time 57.974s
% 58.53/58.93 wallclock.time 57.978s
% 58.53/58.93 status S
% 58.53/58.93
% 58.53/58.93
% 58.53/58.93 Waldmeister states: Goal proved.
% 58.53/58.93 % SZS status Unsatisfiable
%------------------------------------------------------------------------------