TSTP Solution File: LAT009-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n020.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 07:14:39 EDT 2022
% Result : Unsatisfiable 1.53s 1.95s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 22:23:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.61/1.02 ********************************************************************************
% 0.61/1.02 * W A L D M E I S T E R \| \ / \|/ *
% 0.61/1.02 * |/ | \/ | *
% 0.61/1.02 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.61/1.02 * A. Jaeger and B. Loechner | | *
% 0.61/1.02 * <waldmeister@informatik.uni-kl.de> | *
% 0.61/1.02 ********************************************************************************
% 0.61/1.02
% 0.61/1.02
% 0.61/1.02 Goals:
% 0.61/1.02 ------
% 0.61/1.02
% 0.61/1.02 ( 1) meet(join(a,b),join(a,c)) ?=? join(a,meet(b,c))
% 0.61/1.02
% 0.61/1.02 Detected structure: Verband
% 0.61/1.02 ********************************************************************************
% 0.61/1.02 ****************************** COMPLETION - PROOF ******************************
% 0.61/1.02 ********************************************************************************
% 0.61/1.02
% 1.53/1.95 joined goal: 1 meet(join(a,b),join(a,c)) ?= join(a,meet(b,c)) to join(a,meet(c,b))
% 1.53/1.95 goal joined
% 1.53/1.95 % SZS status Unsatisfiable
% 1.53/1.95 #START OF PROOF
% 1.53/1.95 % SZS output start CNFRefutation
% 1.53/1.95 cnf('0.2.0.0',axiom,
% 1.53/1.95 ( X1 = meet(X1,join(X1,X2)) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.2.1.0',plain,
% 1.53/1.95 ( X1 = meet(X1,join(X1,X2)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.53/1.95 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.2.2.0',plain,
% 1.53/1.95 ( meet(X1,join(X1,X2)) = X1 ),
% 1.53/1.95 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_2]).
% 1.53/1.95 cnf('0.4.0.0',axiom,
% 1.53/1.95 ( X1 = join(X1,meet(X1,X2)) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.4.1.0',plain,
% 1.53/1.95 ( X1 = join(X1,meet(X1,X2)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.53/1.95 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.53/1.95 cnf('0.4.2.0',plain,
% 1.53/1.95 ( join(X1,meet(X1,X2)) = X1 ),
% 1.53/1.95 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_4]).
% 1.53/1.95 cnf('0.5.0.0',axiom,
% 1.53/1.95 ( meet(X1,X2) = meet(X2,X1) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.5.1.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X2,X1) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.53/1.95 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.53/1.95 cnf('0.5.2.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X2,X1) ),
% 1.53/1.95 inference(activate,[status(thm)],['0.5.1.0']),
% 1.53/1.95 [equation_1]).
% 1.53/1.95 cnf('0.6.0.0',axiom,
% 1.53/1.95 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.6.1.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.6.0.0']),
% 1.53/1.95 [weight('<5,0,0,[0,0,0,6]>')]).
% 1.53/1.95 cnf('0.6.2.0',plain,
% 1.53/1.95 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_5]).
% 1.53/1.95 cnf('0.7.0.0',axiom,
% 1.53/1.95 ( meet(join(meet(join(X1,X2),X3),X2),join(X3,X1)) = join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.7.1.0',plain,
% 1.53/1.95 ( meet(join(meet(join(X1,X2),X3),X2),join(X3,X1)) = join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.7.0.0']),
% 1.53/1.95 [weight('<6,0,0,[0,0,0,7]>')]).
% 1.53/1.95 cnf('0.7.1.1',plain,
% 1.53/1.95 ( meet(join(X3,X1),join(meet(join(X1,X2),X3),X2)) = join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.7.1.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.7.1.2',plain,
% 1.53/1.95 ( meet(join(X3,X1),join(meet(join(X1,X2),X3),X2)) = join(meet(X2,join(meet(X1,X2),X3)),meet(X3,X1)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.7.1.1','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.1','L')]).
% 1.53/1.95 cnf('0.7.2.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(meet(join(X2,X3),X1),X3)) = join(meet(X3,join(meet(X2,X3),X1)),meet(X1,X2)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.7.1.2',theory(equality)]),
% 1.53/1.95 [u,rule_6]).
% 1.53/1.95 cnf('0.8.0.0',axiom,
% 1.53/1.95 ( join(X1,X2) = join(X2,X1) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.8.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X2,X1) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.8.0.0']),
% 1.53/1.95 [weight('<7,0,0,[0,0,0,8]>')]).
% 1.53/1.95 cnf('0.8.2.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X2,X1) ),
% 1.53/1.95 inference(activate,[status(thm)],['0.8.1.0']),
% 1.53/1.95 [equation_2]).
% 1.53/1.95 cnf('0.9.0.0',axiom,
% 1.53/1.95 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020')).
% 1.53/1.95 cnf('0.9.1.0',plain,
% 1.53/1.95 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.9.0.0']),
% 1.53/1.95 [weight('<8,0,0,[0,0,0,9]>')]).
% 1.53/1.95 cnf('0.9.2.0',plain,
% 1.53/1.95 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_7]).
% 1.53/1.95 cnf('0.10.0.0',plain,
% 1.53/1.95 ( X1 = join(X1,meet(X2,X1)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.10.1.0',plain,
% 1.53/1.95 ( X1 = join(X1,meet(X2,X1)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.10.0.0']),
% 1.53/1.95 [weight('<5,5,4,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.10.2.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,X1)) = X1 ),
% 1.53/1.95 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_8]).
% 1.53/1.95 cnf('0.12.0.0',plain,
% 1.53/1.95 ( X1 = meet(X1,join(X2,X1)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.2.2.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.12.1.0',plain,
% 1.53/1.95 ( X1 = meet(X1,join(X2,X1)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.12.0.0']),
% 1.53/1.95 [weight('<5,8,2,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.12.2.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,X1)) = X1 ),
% 1.53/1.95 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_10]).
% 1.53/1.95 cnf('0.16.0.0',plain,
% 1.53/1.95 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.16.1.0',plain,
% 1.53/1.95 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.16.0.0']),
% 1.53/1.95 [weight('<7,6,2,[1,0,0,1]>')]).
% 1.53/1.95 cnf('0.16.2.0',plain,
% 1.53/1.95 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_14]).
% 1.53/1.95 cnf('0.17.0.0',plain,
% 1.53/1.95 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.17.1.0',plain,
% 1.53/1.95 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.17.0.0']),
% 1.53/1.95 [weight('<7,9,4,[1,0,0,1]>')]).
% 1.53/1.95 cnf('0.17.2.0',plain,
% 1.53/1.95 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_15]).
% 1.53/1.95 cnf('0.19.0.0',plain,
% 1.53/1.95 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.9.2.0','0.10.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.19.1.0',plain,
% 1.53/1.95 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.19.0.0']),
% 1.53/1.95 [weight('<7,10,9,[0,0,0,1]>')]).
% 1.53/1.95 cnf('0.19.2.0',plain,
% 1.53/1.95 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_17]).
% 1.53/1.95 cnf('0.20.0.0',plain,
% 1.53/1.95 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.6.2.0','0.12.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.20.1.0',plain,
% 1.53/1.95 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.20.0.0']),
% 1.53/1.95 [weight('<7,12,6,[0,0,0,1]>')]).
% 1.53/1.95 cnf('0.20.2.0',plain,
% 1.53/1.95 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_18]).
% 1.53/1.95 cnf('0.34.0.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.34.1.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.34.0.0']),
% 1.53/1.95 [weight('<9,6,2,[1,0,0,0]>')]).
% 1.53/1.95 cnf('0.34.2.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_32]).
% 1.53/1.95 cnf('0.37.0.0',plain,
% 1.53/1.95 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.37.1.0',plain,
% 1.53/1.95 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.37.0.0']),
% 1.53/1.95 [weight('<9,9,4,[1,0,0,0]>')]).
% 1.53/1.95 cnf('0.37.2.0',plain,
% 1.53/1.95 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_35]).
% 1.53/1.95 cnf('0.38.0.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.10.2.0','0.9.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.38.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.38.0.0']),
% 1.53/1.95 [weight('<9,10,9,[1,0,0,0]>')]).
% 1.53/1.95 cnf('0.38.2.0',plain,
% 1.53/1.95 ( join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_36]).
% 1.53/1.95 cnf('0.39.0.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.39.1.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.39.0.0']),
% 1.53/1.95 [weight('<9,12,6,[1,0,0,0]>')]).
% 1.53/1.95 cnf('0.39.2.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_37]).
% 1.53/1.95 cnf('0.40.0.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.10.2.0','0.16.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.40.1.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.40.0.0']),
% 1.53/1.95 [weight('<9,16,10,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.40.1.1',plain,
% 1.53/1.95 ( meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.40.1.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('R','L')]).
% 1.53/1.95 cnf('0.40.2.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.40.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_38]).
% 1.53/1.95 cnf('0.45.0.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.12.2.0','0.17.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.45.1.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.45.0.0']),
% 1.53/1.95 [weight('<9,17,12,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.45.1.1',plain,
% 1.53/1.95 ( join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.45.1.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('R','L')]).
% 1.53/1.95 cnf('0.45.2.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.45.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_43]).
% 1.53/1.95 cnf('0.54.0.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.12.2.0','0.19.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.54.1.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.54.0.0']),
% 1.53/1.95 [weight('<9,19,12,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.54.1.1',plain,
% 1.53/1.95 ( join(meet(X1,X2),X3) = meet(join(X2,X3),join(meet(X1,X2),X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.54.1.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('R','L')]).
% 1.53/1.95 cnf('0.54.2.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(meet(X3,X1),X2)) = join(meet(X3,X1),X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.54.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_52]).
% 1.53/1.95 cnf('0.58.0.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.10.2.0','0.20.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.58.1.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.58.0.0']),
% 1.53/1.95 [weight('<9,20,10,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.58.1.1',plain,
% 1.53/1.95 ( meet(join(X1,X2),X3) = join(meet(X2,X3),meet(join(X1,X2),X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.58.1.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('R','L')]).
% 1.53/1.95 cnf('0.58.2.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.58.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_56]).
% 1.53/1.95 cnf('0.90.0.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,meet(X2,join(meet(X2,X1),X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.34.2.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2.2.1','L')]).
% 1.53/1.95 cnf('0.90.1.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,meet(X2,join(meet(X2,X1),X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.90.0.0']),
% 1.53/1.95 [weight('<9,34,5,[1,0,0,5]>')]).
% 1.53/1.95 cnf('0.90.2.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.90.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_88]).
% 1.53/1.95 cnf('0.93.0.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,join(X2,meet(join(X2,X1),X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.37.2.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2.2.1','L')]).
% 1.53/1.95 cnf('0.93.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,join(X2,meet(join(X2,X1),X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.93.0.0']),
% 1.53/1.95 [weight('<9,37,8,[1,0,0,5]>')]).
% 1.53/1.95 cnf('0.93.2.0',plain,
% 1.53/1.95 ( join(X1,join(X2,meet(join(X2,X1),X3))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.93.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_91]).
% 1.53/1.95 cnf('0.94.0.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.38.2.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2.2.2','L')]).
% 1.53/1.95 cnf('0.94.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.94.0.0']),
% 1.53/1.95 [weight('<9,38,8,[1,0,0,6]>')]).
% 1.53/1.95 cnf('0.94.2.0',plain,
% 1.53/1.95 ( join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_92]).
% 1.53/1.95 cnf('0.95.0.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.39.2.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2.2.2','L')]).
% 1.53/1.95 cnf('0.95.1.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.95.0.0']),
% 1.53/1.95 [weight('<9,39,5,[1,0,0,6]>')]).
% 1.53/1.95 cnf('0.95.2.0',plain,
% 1.53/1.95 ( meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_93]).
% 1.53/1.95 cnf('0.96.0.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.40.2.0','0.2.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.96.1.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.96.0.0']),
% 1.53/1.95 [weight('<9,40,2,[1,0,0,1]>')]).
% 1.53/1.95 cnf('0.96.2.0',plain,
% 1.53/1.95 ( join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.96.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_94]).
% 1.53/1.95 cnf('0.106.0.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.45.2.0','0.4.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.106.1.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.106.0.0']),
% 1.53/1.95 [weight('<9,45,4,[1,0,0,1]>')]).
% 1.53/1.95 cnf('0.106.2.0',plain,
% 1.53/1.95 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_104]).
% 1.53/1.95 cnf('0.113.0.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),meet(X2,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.54.2.0','0.4.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.113.1.0',plain,
% 1.53/1.95 ( join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),meet(X2,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.113.0.0']),
% 1.53/1.95 [weight('<9,54,4,[1,0,0,1]>')]).
% 1.53/1.95 cnf('0.113.2.0',plain,
% 1.53/1.95 ( meet(X1,join(meet(X2,X1),meet(X1,X3))) = join(meet(X2,X1),meet(X1,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.113.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_109]).
% 1.53/1.95 cnf('0.116.0.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),join(X2,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.58.2.0','0.2.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.1','L')]).
% 1.53/1.95 cnf('0.116.1.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),join(X2,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.116.0.0']),
% 1.53/1.95 [weight('<9,58,2,[1,0,0,1]>')]).
% 1.53/1.95 cnf('0.116.2.0',plain,
% 1.53/1.95 ( join(X1,meet(join(X2,X1),join(X1,X3))) = meet(join(X2,X1),join(X1,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.116.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_112]).
% 1.53/1.95 cnf('0.124.0.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,meet(join(X2,X1),join(X2,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.93.2.0','0.96.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.124.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,meet(join(X2,X1),join(X2,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.124.0.0']),
% 1.53/1.95 [weight('<9,96,93,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.124.2.0',plain,
% 1.53/1.95 ( join(X1,meet(join(X2,X1),join(X2,X3))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_120]).
% 1.53/1.95 cnf('0.125.0.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,meet(join(X2,X3),join(X2,X1))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.94.2.0','0.96.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.125.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,meet(join(X2,X3),join(X2,X1))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.125.0.0']),
% 1.53/1.95 [weight('<9,96,94,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.125.2.0',plain,
% 1.53/1.95 ( join(X1,meet(join(X2,X3),join(X2,X1))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_121]).
% 1.53/1.95 cnf('0.127.0.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,join(meet(X2,X1),meet(X2,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.90.2.0','0.106.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.127.1.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,join(meet(X2,X1),meet(X2,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.127.0.0']),
% 1.53/1.95 [weight('<9,106,90,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.127.2.0',plain,
% 1.53/1.95 ( meet(X1,join(meet(X2,X1),meet(X2,X3))) = meet(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.127.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_122]).
% 1.53/1.95 cnf('0.133.0.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.95.2.0','0.113.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.133.1.0',plain,
% 1.53/1.95 ( meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.133.0.0']),
% 1.53/1.95 [weight('<9,113,95,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.133.2.0',plain,
% 1.53/1.95 ( meet(X1,join(meet(X2,X3),meet(X3,X1))) = meet(X1,X3) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_127]).
% 1.53/1.95 cnf('0.136.0.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,meet(join(X1,X2),join(X2,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.37.2.0','0.116.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.136.1.0',plain,
% 1.53/1.95 ( join(X1,X2) = join(X1,meet(join(X1,X2),join(X2,X3))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.136.0.0']),
% 1.53/1.95 [weight('<9,116,37,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.136.2.0',plain,
% 1.53/1.95 ( join(X1,meet(join(X1,X2),join(X2,X3))) = join(X1,X2) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.136.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_130]).
% 1.53/1.95 cnf('0.143.0.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(meet(join(X2,X3),X1),X2)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.127.2.0','0.125.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.143.1.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(meet(join(X2,X3),X1),X2)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.143.0.0']),
% 1.53/1.95 [weight('<9,127,125,[1,0,0,2]>')]).
% 1.53/1.95 cnf('0.143.1.1',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(join(X2,X3),X1))) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.143.1.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.2','L')]).
% 1.53/1.95 cnf('0.143.2.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,meet(join(X2,X3),X1))) = meet(X1,join(X2,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.143.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_137]).
% 1.53/1.95 cnf('0.148.0.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = join(X1,meet(join(meet(X2,X3),X1),X3)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.124.2.0','0.133.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.148.1.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = join(X1,meet(join(meet(X2,X3),X1),X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.148.0.0']),
% 1.53/1.95 [weight('<9,133,124,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.148.1.1',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = join(X1,meet(X3,join(meet(X2,X3),X1))) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.148.1.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.2','L')]).
% 1.53/1.95 cnf('0.148.2.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,join(meet(X3,X2),X1))) = join(X1,meet(X3,X2)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.148.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_142]).
% 1.53/1.95 cnf('0.151.0.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = join(X1,meet(join(X1,meet(X2,X3)),X3)) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.136.2.0','0.133.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.151.1.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = join(X1,meet(join(X1,meet(X2,X3)),X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.151.0.0']),
% 1.53/1.95 [weight('<9,136,133,[1,0,0,2]>')]).
% 1.53/1.95 cnf('0.151.1.1',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = join(X1,meet(X3,join(X1,meet(X2,X3)))) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.151.1.0','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.2','L')]).
% 1.53/1.95 cnf('0.151.2.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,join(X1,meet(X3,X2)))) = join(X1,meet(X3,X2)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.151.1.1',theory(equality)]),
% 1.53/1.95 [x,rule_145]).
% 1.53/1.95 cnf('0.154.0.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(meet(join(X2,X3),X1),X3)) = join(meet(X3,join(meet(X2,X3),X1)),meet(X1,X2)) ),
% 1.53/1.95 inference(interreduction_right,[status(thm)],['0.7.2.0'])).
% 1.53/1.95 cnf('0.154.1.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(meet(join(X2,X3),X1),X3)) = join(meet(X3,join(meet(X2,X3),X1)),meet(X1,X2)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.154.0.0']),
% 1.53/1.95 [weight('<11,7,8,[0,0,0,0]>')]).
% 1.53/1.95 cnf('0.154.1.1',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))) = join(meet(X3,join(meet(X2,X3),X1)),meet(X1,X2)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.154.1.0','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.154.1.2',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.154.1.1','0.8.2.0',theory(equality)]),
% 1.53/1.95 [pos('R','L')]).
% 1.53/1.95 cnf('0.154.2.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.154.1.2',theory(equality)]),
% 1.53/1.95 [u,rule_146]).
% 1.53/1.95 cnf('0.553.0.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,meet(join(X2,X3),join(X1,X4)))) = meet(X1,meet(join(X1,X4),join(X2,X3))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.16.2.0','0.143.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.553.0.1',plain,
% 1.53/1.95 ( meet(X1,join(X2,meet(join(X2,X3),join(X1,X4)))) = meet(X1,join(X2,X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.553.0.0','0.16.2.0',theory(equality)]),
% 1.53/1.95 [pos('R','L')]).
% 1.53/1.95 cnf('0.553.1.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,meet(join(X2,X3),join(X1,X4)))) = meet(X1,join(X2,X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.553.0.1']),
% 1.53/1.95 [weight('<11,143,16,[0,0,0,2]>')]).
% 1.53/1.95 cnf('0.553.2.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,meet(join(X2,X3),join(X1,X4)))) = meet(X1,join(X2,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.553.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_545]).
% 1.53/1.95 cnf('0.554.0.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(X2,join(meet(X2,X3),meet(X1,join(meet(X3,X1),X2))))) ),
% 1.53/1.95 inference(cp,[status(thm)],['0.553.2.0','0.154.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2.2','L')]).
% 1.53/1.95 cnf('0.554.0.1',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(meet(X3,X1),X2)))) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.554.0.0','0.17.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.2','L')]).
% 1.53/1.95 cnf('0.554.0.2',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X3,X1))) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.554.0.1','0.148.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.2','L')]).
% 1.53/1.95 cnf('0.554.1.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X3,X1))) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.554.0.2']),
% 1.53/1.95 [weight('<7,553,154,[1,0,0,4]>')]).
% 1.53/1.95 cnf('0.554.2.0',plain,
% 1.53/1.95 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.554.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_546]).
% 1.53/1.95 cnf('0.557.0.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,join(X1,meet(X3,X2)))) = join(X1,meet(X3,X2)) ),
% 1.53/1.95 inference(interreduction_right,[status(thm)],['0.151.2.0'])).
% 1.53/1.95 cnf('0.557.0.1',plain,
% 1.53/1.95 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.557.0.0','0.554.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('0.557.1.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.557.0.1']),
% 1.53/1.95 [weight('<7,151,554,[0,0,0,0]>')]).
% 1.53/1.95 cnf('0.557.2.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.557.1.0',theory(equality)]),
% 1.53/1.95 [u,rule_549]).
% 1.53/1.95 cnf('0.558.0.0',plain,
% 1.53/1.95 ( join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)) ),
% 1.53/1.95 inference(interreduction_right,[status(thm)],['0.96.2.0'])).
% 1.53/1.95 cnf('0.558.0.1',plain,
% 1.53/1.95 ( join(X1,meet(X3,join(X1,X2))) = meet(join(X1,X2),join(X1,X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.558.0.0','0.557.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.558.0.2',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['0.558.0.1','0.557.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('0.558.1.0',plain,
% 1.53/1.95 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 1.53/1.95 inference(weigh,[status(thm)],['0.558.0.2']),
% 1.53/1.95 [weight('<7,96,557,[0,0,0,0]>')]).
% 1.53/1.95 cnf('0.558.2.0',plain,
% 1.53/1.95 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,X3)) ),
% 1.53/1.95 inference(orient,[status(thm)],['0.558.1.0',theory(equality)]),
% 1.53/1.95 [x,rule_550]).
% 1.53/1.95 cnf('1.0.0.0',conjecture,
% 1.53/1.95 ( meet(join(a,b),join(a,c)) = join(a,meet(b,c)) ),
% 1.53/1.95 file('/tmp/WALDMEISTER_25524_n020',conjecture_1)).
% 1.53/1.95 cnf('1.0.0.1',plain,
% 1.53/1.95 ( join(a,meet(b,c)) = join(a,meet(b,c)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['1.0.0.0','0.558.2.0',theory(equality)]),
% 1.53/1.95 [pos('L','L')]).
% 1.53/1.95 cnf('1.0.0.2',plain,
% 1.53/1.95 ( join(a,meet(c,b)) = join(a,meet(b,c)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['1.0.0.1','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('L.2','L')]).
% 1.53/1.95 cnf('1.0.0.3',plain,
% 1.53/1.95 ( join(a,meet(c,b)) = join(a,meet(c,b)) ),
% 1.53/1.95 inference(reduction,[status(thm)],['1.0.0.2','0.5.2.0',theory(equality)]),
% 1.53/1.95 [pos('R.2','L')]).
% 1.53/1.95 cnf('1.0.0.4',plain,
% 1.53/1.95 ( $true ),
% 1.53/1.95 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 1.53/1.95 [conjecture_1]).
% 1.53/1.95
% 1.53/1.95 Proved Goals:
% 1.53/1.95 No. 1: meet(join(a,b),join(a,c)) ?= join(a,meet(b,c)) joined, current: join(a,meet(c,b)) = join(a,meet(c,b))
% 1.53/1.95 1 goal was specified, which was proved.
% 1.53/1.95 % SZS output end CNFRefutation
% 1.53/1.95 #END OF PROOF
% 1.53/1.95
% 1.53/1.95 Problem WALDMEISTER_25524_n020
% 1.53/1.95 CPs.gen 256392
% 1.53/1.95 CPs.reexp 0
% 1.53/1.95 Select 9714
% 1.53/1.95 R 550
% 1.53/1.95 E 8
% 1.53/1.95 vsize 8.5M
% 1.53/1.95 rss 4.0M
% 1.53/1.95 process.time 0.928s
% 1.53/1.95 wallclock.time 0.929s
% 1.53/1.95 status S
% 1.53/1.95
% 1.53/1.95
% 1.53/1.95 Waldmeister states: Goal proved.
% 1.53/1.95 % SZS status Unsatisfiable
%------------------------------------------------------------------------------