%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT155-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n007.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 07:15:24 EDT 2022
% Result : Unsatisfiable 67.57s 68.02s
% Output : CNFRefutation 67.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT155-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : woody %s
% 0.12/0.34 % Computer : n007.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 15:52:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.99 * |/ | \/ | *
% 0.59/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.99 * A. Jaeger and B. Loechner | | *
% 0.59/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Goals:
% 0.59/0.99 ------
% 0.59/0.99
% 0.59/0.99 ( 1) meet(a,join(b,meet(a,c))) ?=? meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c)))))
% 0.59/0.99
% 0.59/0.99 Detected structure: Verband
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 67.57/68.02 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)))
% 67.57/68.02 goal joined
% 67.57/68.02 % SZS status Unsatisfiable
% 67.57/68.02 #START OF PROOF
% 67.57/68.02 % SZS output start CNFRefutation
% 67.57/68.02 cnf('0.2.0.0',axiom,
% 67.57/68.02 ( X1 = meet(X1,join(X1,X2)) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.2.1.0',plain,
% 67.57/68.02 ( X1 = meet(X1,join(X1,X2)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.2.0.0']),
% 67.57/68.02 [weight('<1,0,0,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.2.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X1,X2)) = X1 ),
% 67.57/68.02 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_2]).
% 67.57/68.02 cnf('0.3.0.0',axiom,
% 67.57/68.02 ( X1 = join(X1,X1) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.3.1.0',plain,
% 67.57/68.02 ( X1 = join(X1,X1) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.3.0.0']),
% 67.57/68.02 [weight('<2,0,0,[0,0,0,3]>')]).
% 67.57/68.02 cnf('0.3.2.0',plain,
% 67.57/68.02 ( join(X1,X1) = X1 ),
% 67.57/68.02 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_3]).
% 67.57/68.02 cnf('0.4.0.0',axiom,
% 67.57/68.02 ( X1 = join(X1,meet(X1,X2)) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.4.1.0',plain,
% 67.57/68.02 ( X1 = join(X1,meet(X1,X2)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.4.0.0']),
% 67.57/68.02 [weight('<3,0,0,[0,0,0,4]>')]).
% 67.57/68.02 cnf('0.4.2.0',plain,
% 67.57/68.02 ( join(X1,meet(X1,X2)) = X1 ),
% 67.57/68.02 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_4]).
% 67.57/68.02 cnf('0.5.0.0',axiom,
% 67.57/68.02 ( meet(X1,X2) = meet(X2,X1) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.5.1.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X2,X1) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.5.0.0']),
% 67.57/68.02 [weight('<4,0,0,[0,0,0,5]>')]).
% 67.57/68.02 cnf('0.5.2.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X2,X1) ),
% 67.57/68.02 inference(activate,[status(thm)],['0.5.1.0']),
% 67.57/68.02 [equation_1]).
% 67.57/68.02 cnf('0.6.0.0',axiom,
% 67.57/68.02 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.6.1.0',plain,
% 67.57/68.02 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.6.0.0']),
% 67.57/68.02 [weight('<5,0,0,[0,0,0,6]>')]).
% 67.57/68.02 cnf('0.6.2.0',plain,
% 67.57/68.02 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_5]).
% 67.57/68.02 cnf('0.7.0.0',axiom,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.7.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.7.0.0']),
% 67.57/68.02 [weight('<6,0,0,[0,0,0,7]>')]).
% 67.57/68.02 cnf('0.7.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_6]).
% 67.57/68.02 cnf('0.8.0.0',axiom,
% 67.57/68.02 ( join(X1,X2) = join(X2,X1) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.8.1.0',plain,
% 67.57/68.02 ( join(X1,X2) = join(X2,X1) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.8.0.0']),
% 67.57/68.02 [weight('<7,0,0,[0,0,0,8]>')]).
% 67.57/68.02 cnf('0.8.2.0',plain,
% 67.57/68.02 ( join(X1,X2) = join(X2,X1) ),
% 67.57/68.02 inference(activate,[status(thm)],['0.8.1.0']),
% 67.57/68.02 [equation_2]).
% 67.57/68.02 cnf('0.9.0.0',axiom,
% 67.57/68.02 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007')).
% 67.57/68.02 cnf('0.9.1.0',plain,
% 67.57/68.02 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.9.0.0']),
% 67.57/68.02 [weight('<8,0,0,[0,0,0,9]>')]).
% 67.57/68.02 cnf('0.9.2.0',plain,
% 67.57/68.02 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_7]).
% 67.57/68.02 cnf('0.10.0.0',plain,
% 67.57/68.02 ( X1 = join(X1,meet(X2,X1)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.10.1.0',plain,
% 67.57/68.02 ( X1 = join(X1,meet(X2,X1)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.10.0.0']),
% 67.57/68.02 [weight('<5,5,4,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.10.2.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,X1)) = X1 ),
% 67.57/68.02 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_8]).
% 67.57/68.02 cnf('0.12.0.0',plain,
% 67.57/68.02 ( X1 = meet(X1,join(X2,X1)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.2.2.0','0.8.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.12.1.0',plain,
% 67.57/68.02 ( X1 = meet(X1,join(X2,X1)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.12.0.0']),
% 67.57/68.02 [weight('<5,8,2,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.12.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,X1)) = X1 ),
% 67.57/68.02 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_10]).
% 67.57/68.02 cnf('0.13.0.0',plain,
% 67.57/68.02 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.9.2.0','0.3.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.13.1.0',plain,
% 67.57/68.02 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.13.0.0']),
% 67.57/68.02 [weight('<5,9,3,[1,0,0,1]>')]).
% 67.57/68.02 cnf('0.13.2.0',plain,
% 67.57/68.02 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_11]).
% 67.57/68.02 cnf('0.14.0.0',plain,
% 67.57/68.02 ( join(X1,X2) = join(join(X1,X2),X1) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.10.2.0','0.2.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.14.0.1',plain,
% 67.57/68.02 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.14.0.0','0.9.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.14.1.0',plain,
% 67.57/68.02 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.14.0.1']),
% 67.57/68.02 [weight('<5,10,2,[1,0,0,2]>')]).
% 67.57/68.02 cnf('0.14.2.0',plain,
% 67.57/68.02 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_12]).
% 67.57/68.02 cnf('0.16.0.0',plain,
% 67.57/68.02 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.16.1.0',plain,
% 67.57/68.02 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.16.0.0']),
% 67.57/68.02 [weight('<7,6,2,[1,0,0,1]>')]).
% 67.57/68.02 cnf('0.16.2.0',plain,
% 67.57/68.02 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_14]).
% 67.57/68.02 cnf('0.17.0.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.17.1.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.17.0.0']),
% 67.57/68.02 [weight('<7,9,4,[1,0,0,1]>')]).
% 67.57/68.02 cnf('0.17.2.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_15]).
% 67.57/68.02 cnf('0.19.0.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.9.2.0','0.10.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.19.1.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.19.0.0']),
% 67.57/68.02 [weight('<7,10,9,[0,0,0,1]>')]).
% 67.57/68.02 cnf('0.19.2.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_17]).
% 67.57/68.02 cnf('0.20.0.0',plain,
% 67.57/68.02 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.6.2.0','0.12.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.20.1.0',plain,
% 67.57/68.02 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.20.0.0']),
% 67.57/68.02 [weight('<7,12,6,[0,0,0,1]>')]).
% 67.57/68.02 cnf('0.20.2.0',plain,
% 67.57/68.02 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_18]).
% 67.57/68.02 cnf('0.21.0.0',plain,
% 67.57/68.02 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.12.2.0','0.9.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.21.1.0',plain,
% 67.57/68.02 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.21.0.0']),
% 67.57/68.02 [weight('<7,12,9,[1,0,0,2]>')]).
% 67.57/68.02 cnf('0.21.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,X1))) = X1 ),
% 67.57/68.02 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_19]).
% 67.57/68.02 cnf('0.22.0.0',plain,
% 67.57/68.02 ( join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.9.2.0','0.14.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.22.0.1',plain,
% 67.57/68.02 ( join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.22.0.0','0.9.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.22.0.2',plain,
% 67.57/68.02 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.22.0.1','0.9.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.22.1.0',plain,
% 67.57/68.02 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.22.0.2']),
% 67.57/68.02 [weight('<7,14,9,[0,0,0,1]>')]).
% 67.57/68.02 cnf('0.22.2.0',plain,
% 67.57/68.02 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_20]).
% 67.57/68.02 cnf('0.33.0.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.20.2.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.33.1.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.33.0.0']),
% 67.57/68.02 [weight('<7,20,5,[1,0,0,2]>')]).
% 67.57/68.02 cnf('0.33.2.0',plain,
% 67.57/68.02 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_31]).
% 67.57/68.02 cnf('0.37.0.0',plain,
% 67.57/68.02 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 67.57/68.02 [pos('L','L')]).
% 67.57/68.02 cnf('0.37.1.0',plain,
% 67.57/68.02 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.37.0.0']),
% 67.57/68.02 [weight('<9,9,4,[1,0,0,0]>')]).
% 67.57/68.02 cnf('0.37.2.0',plain,
% 67.57/68.02 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_35]).
% 67.57/68.02 cnf('0.39.0.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 67.57/68.02 [pos('L','L')]).
% 67.57/68.02 cnf('0.39.1.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.39.0.0']),
% 67.57/68.02 [weight('<9,12,6,[1,0,0,0]>')]).
% 67.57/68.02 cnf('0.39.2.0',plain,
% 67.57/68.02 ( meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_37]).
% 67.57/68.02 cnf('0.45.0.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.12.2.0','0.17.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.45.1.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.45.0.0']),
% 67.57/68.02 [weight('<9,17,12,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.45.1.1',plain,
% 67.57/68.02 ( join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.45.1.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.45.2.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.45.1.1',theory(equality)]),
% 67.57/68.02 [x,rule_43]).
% 67.57/68.02 cnf('0.54.0.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.12.2.0','0.19.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.54.1.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.54.0.0']),
% 67.57/68.02 [weight('<9,19,12,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.54.1.1',plain,
% 67.57/68.02 ( join(meet(X1,X2),X3) = meet(join(X2,X3),join(meet(X1,X2),X3)) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.54.1.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.54.2.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),join(meet(X3,X1),X2)) = join(meet(X3,X1),X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.54.1.1',theory(equality)]),
% 67.57/68.02 [x,rule_52]).
% 67.57/68.02 cnf('0.58.0.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.10.2.0','0.20.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.58.1.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.58.0.0']),
% 67.57/68.02 [weight('<9,20,10,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.58.1.1',plain,
% 67.57/68.02 ( meet(join(X1,X2),X3) = join(meet(X2,X3),meet(join(X1,X2),X3)) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.58.1.0','0.8.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.58.2.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.58.1.1',theory(equality)]),
% 67.57/68.02 [x,rule_56]).
% 67.57/68.02 cnf('0.68.0.0',plain,
% 67.57/68.02 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.21.2.0','0.22.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.68.1.0',plain,
% 67.57/68.02 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.68.0.0']),
% 67.57/68.02 [weight('<9,22,21,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.68.2.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_66]).
% 67.57/68.02 cnf('0.88.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X3,X1)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.10.2.0','0.33.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.88.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X3,X1)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.88.0.0']),
% 67.57/68.02 [weight('<9,33,10,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.88.1.1',plain,
% 67.57/68.02 ( meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X1,join(X2,X3))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.88.1.0','0.8.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.88.2.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.88.1.1',theory(equality)]),
% 67.57/68.02 [x,rule_86]).
% 67.57/68.02 cnf('0.95.0.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.39.2.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.2','L')]).
% 67.57/68.02 cnf('0.95.1.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.95.0.0']),
% 67.57/68.02 [weight('<9,39,5,[1,0,0,6]>')]).
% 67.57/68.02 cnf('0.95.2.0',plain,
% 67.57/68.02 ( meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_93]).
% 67.57/68.02 cnf('0.106.0.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.45.2.0','0.4.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.106.1.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.106.0.0']),
% 67.57/68.02 [weight('<9,45,4,[1,0,0,1]>')]).
% 67.57/68.02 cnf('0.106.2.0',plain,
% 67.57/68.02 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_104]).
% 67.57/68.02 cnf('0.115.0.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),meet(X3,X2))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.54.2.0','0.10.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.115.1.0',plain,
% 67.57/68.02 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),meet(X3,X2))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.115.0.0']),
% 67.57/68.02 [weight('<9,54,10,[1,0,0,1]>')]).
% 67.57/68.02 cnf('0.115.2.0',plain,
% 67.57/68.02 ( meet(X1,join(meet(X2,X1),meet(X3,X1))) = join(meet(X2,X1),meet(X3,X1)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.115.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_111]).
% 67.57/68.02 cnf('0.116.0.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),join(X2,X3))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.58.2.0','0.2.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.1','L')]).
% 67.57/68.02 cnf('0.116.1.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),join(X2,X3))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.116.0.0']),
% 67.57/68.02 [weight('<9,58,2,[1,0,0,1]>')]).
% 67.57/68.02 cnf('0.116.2.0',plain,
% 67.57/68.02 ( join(X1,meet(join(X2,X1),join(X1,X3))) = meet(join(X2,X1),join(X1,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.116.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_112]).
% 67.57/68.02 cnf('0.120.0.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.68.2.0','0.4.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2','L')]).
% 67.57/68.02 cnf('0.120.1.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.120.0.0']),
% 67.57/68.02 [weight('<9,68,4,[1,0,0,6]>')]).
% 67.57/68.02 cnf('0.120.1.1',plain,
% 67.57/68.02 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,meet(X2,X3))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.120.1.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.120.2.0',plain,
% 67.57/68.02 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.120.1.1',theory(equality)]),
% 67.57/68.02 [x,rule_116]).
% 67.57/68.02 cnf('0.124.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,X1)))) = meet(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.7.2.0','0.88.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2','L')]).
% 67.57/68.02 cnf('0.124.0.1',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.124.0.0','0.3.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.2','L')]).
% 67.57/68.02 cnf('0.124.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.124.0.1']),
% 67.57/68.02 [weight('<9,88,7,[0,0,0,4]>')]).
% 67.57/68.02 cnf('0.124.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X3,X1))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_120]).
% 67.57/68.02 cnf('0.129.0.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,join(meet(X2,X3),meet(X2,X1))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.95.2.0','0.106.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.129.1.0',plain,
% 67.57/68.02 ( meet(X1,X2) = meet(X1,join(meet(X2,X3),meet(X2,X1))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.129.0.0']),
% 67.57/68.02 [weight('<9,106,95,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.129.2.0',plain,
% 67.57/68.02 ( meet(X1,join(meet(X2,X3),meet(X2,X1))) = meet(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.129.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_124]).
% 67.57/68.02 cnf('0.137.0.0',plain,
% 67.57/68.02 ( join(X1,X2) = join(X1,meet(join(X1,X2),join(X2,X3))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.37.2.0','0.116.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.137.1.0',plain,
% 67.57/68.02 ( join(X1,X2) = join(X1,meet(join(X1,X2),join(X2,X3))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.137.0.0']),
% 67.57/68.02 [weight('<9,116,37,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.137.2.0',plain,
% 67.57/68.02 ( join(X1,meet(join(X1,X2),join(X2,X3))) = join(X1,X2) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_131]).
% 67.57/68.02 cnf('0.142.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.124.2.0','0.8.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.2','L')]).
% 67.57/68.02 cnf('0.142.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.142.0.0']),
% 67.57/68.02 [weight('<9,124,8,[1,0,0,6]>')]).
% 67.57/68.02 cnf('0.142.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X3,X1))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_136]).
% 67.57/68.02 cnf('0.153.0.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,X3)) = join(X1,meet(join(X1,meet(X2,X3)),X2)) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.137.2.0','0.129.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.153.1.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,X3)) = join(X1,meet(join(X1,meet(X2,X3)),X2)) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.153.0.0']),
% 67.57/68.02 [weight('<9,137,129,[1,0,0,2]>')]).
% 67.57/68.02 cnf('0.153.1.1',plain,
% 67.57/68.02 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,join(X1,meet(X2,X3)))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.153.1.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('R.2','L')]).
% 67.57/68.02 cnf('0.153.2.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,join(X1,meet(X2,X3)))) = join(X1,meet(X2,X3)) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.153.1.1',theory(equality)]),
% 67.57/68.02 [x,rule_147]).
% 67.57/68.02 cnf('0.159.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,join(X4,X2))))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.7.2.0','0.14.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.2.2','L')]).
% 67.57/68.02 cnf('0.159.0.1',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,join(X4,X2))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.159.0.0','0.7.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.159.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,join(X4,X2))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.159.0.1']),
% 67.57/68.02 [weight('<11,14,7,[0,0,0,10]>')]).
% 67.57/68.02 cnf('0.159.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X1,join(X4,X2))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.159.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_151]).
% 67.57/68.02 cnf('0.488.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X2,join(X1,X4))))) = meet(X1,meet(join(X1,X4),join(X2,meet(X3,join(X1,X4))))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.16.2.0','0.124.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.488.0.1',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X2,join(X1,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.488.0.0','0.16.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.488.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X2,join(X1,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.488.0.1']),
% 67.57/68.02 [weight('<11,124,16,[0,0,0,2]>')]).
% 67.57/68.02 cnf('0.488.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(X2,join(X1,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.488.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_480]).
% 67.57/68.02 cnf('0.616.0.0',plain,
% 67.57/68.02 ( meet(X1,join(join(X2,X3),meet(X4,join(X1,X2)))) = meet(X1,join(join(X2,X3),meet(X4,join(X1,join(X2,X3))))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.159.2.0','0.13.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.2.2','L')]).
% 67.57/68.02 cnf('0.616.0.1',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(join(X2,X3),meet(X4,join(X1,join(X2,X3))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.616.0.0','0.9.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.616.0.2',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(join(X2,X3),meet(X4,X1))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.616.0.1','0.142.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.616.0.3',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(X2,join(X3,meet(X4,X1)))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.616.0.2','0.9.2.0',theory(equality)]),
% 67.57/68.02 [pos('R.2','L')]).
% 67.57/68.02 cnf('0.616.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(X2,join(X3,meet(X4,X1)))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.616.0.3']),
% 67.57/68.02 [weight('<11,159,13,[1,0,0,8]>')]).
% 67.57/68.02 cnf('0.616.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(X2,join(X3,meet(X4,X1)))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.616.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_608]).
% 67.57/68.02 cnf('0.772.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,X1)))) = meet(X1,join(X2,join(meet(X4,join(X1,X2)),X3))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.616.2.0','0.8.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2','L')]).
% 67.57/68.02 cnf('0.772.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,X1)))) = meet(X1,join(X2,join(meet(X4,join(X1,X2)),X3))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.772.0.0']),
% 67.57/68.02 [weight('<11,616,8,[1,0,0,4]>')]).
% 67.57/68.02 cnf('0.772.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(meet(X3,join(X1,X2)),X4))) = meet(X1,join(X2,join(X4,meet(X3,X1)))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.772.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_764]).
% 67.57/68.02 cnf('0.788.0.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,X1)))) = meet(X1,join(X2,join(meet(X4,join(X2,X1)),X3))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.772.2.0','0.8.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.1.2','L')]).
% 67.57/68.02 cnf('0.788.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(X3,meet(X4,X1)))) = meet(X1,join(X2,join(meet(X4,join(X2,X1)),X3))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.788.0.0']),
% 67.57/68.02 [weight('<11,772,8,[1,0,0,7]>')]).
% 67.57/68.02 cnf('0.788.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,join(meet(X3,join(X2,X1)),X4))) = meet(X1,join(X2,join(X4,meet(X3,X1)))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.788.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_780]).
% 67.57/68.02 cnf('0.1815.0.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,join(meet(X3,X2),meet(X4,X2)))) = join(X1,meet(X2,join(X1,join(meet(X3,X2),meet(X4,X2))))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.153.2.0','0.115.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2.2','L')]).
% 67.57/68.02 cnf('0.1815.0.1',plain,
% 67.57/68.02 ( join(X1,join(meet(X3,X2),meet(X4,X2))) = join(X1,meet(X2,join(X1,join(meet(X3,X2),meet(X4,X2))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.1815.0.0','0.115.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.1815.1.0',plain,
% 67.57/68.02 ( join(X1,join(meet(X3,X2),meet(X4,X2))) = join(X1,meet(X2,join(X1,join(meet(X3,X2),meet(X4,X2))))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.1815.0.1']),
% 67.57/68.02 [weight('<13,153,115,[1,0,0,6]>')]).
% 67.57/68.02 cnf('0.1815.2.0',plain,
% 67.57/68.02 ( join(X1,meet(X2,join(X1,join(meet(X3,X2),meet(X4,X2))))) = join(X1,join(meet(X3,X2),meet(X4,X2))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.1815.1.0',theory(equality)]),
% 67.57/68.02 [x,rule_1806]).
% 67.57/68.02 cnf('0.3897.0.0',plain,
% 67.57/68.02 ( meet(meet(X1,join(X2,X3)),join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4)))) = meet(meet(X1,join(X2,X3)),join(X2,meet(X3,join(X2,join(X4,meet(X1,X3)))))) ),
% 67.57/68.02 inference(cp,[status(thm)],['0.488.2.0','0.788.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2','L')]).
% 67.57/68.02 cnf('0.3897.0.1',plain,
% 67.57/68.02 ( meet(X1,meet(join(X2,X3),join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4))))) = meet(meet(X1,join(X2,X3)),join(X2,meet(X3,join(X2,join(X4,meet(X1,X3)))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.3897.0.0','0.6.2.0',theory(equality)]),
% 67.57/68.02 [pos('L','L')]).
% 67.57/68.02 cnf('0.3897.0.2',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4)))) = meet(meet(X1,join(X2,X3)),join(X2,meet(X3,join(X2,join(X4,meet(X1,X3)))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.3897.0.1','0.120.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2','L')]).
% 67.57/68.02 cnf('0.3897.0.3',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4)))) = meet(X1,meet(join(X2,X3),join(X2,meet(X3,join(X2,join(X4,meet(X1,X3))))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.3897.0.2','0.6.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('0.3897.0.4',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4)))) = meet(X1,join(X2,meet(X3,join(X2,join(X4,meet(X1,X3)))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['0.3897.0.3','0.120.2.0',theory(equality)]),
% 67.57/68.02 [pos('R.2','L')]).
% 67.57/68.02 cnf('0.3897.1.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4)))) = meet(X1,join(X2,meet(X3,join(X2,join(X4,meet(X1,X3)))))) ),
% 67.57/68.02 inference(weigh,[status(thm)],['0.3897.0.4']),
% 67.57/68.02 [weight('<13,788,488,[0,0,0,4]>')]).
% 67.57/68.02 cnf('0.3897.2.0',plain,
% 67.57/68.02 ( meet(X1,join(X2,meet(X3,join(meet(X1,join(X2,X3)),X4)))) = meet(X1,join(X2,meet(X3,join(X2,join(X4,meet(X1,X3)))))) ),
% 67.57/68.02 inference(orient,[status(thm)],['0.3897.1.0',theory(equality)]),
% 67.57/68.02 [u,rule_3885]).
% 67.57/68.02 cnf('1.0.0.0',conjecture,
% 67.57/68.02 ( meet(a,join(b,meet(a,c))) = meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) ),
% 67.57/68.02 file('/tmp/WALDMEISTER_20173_n007',conjecture_1)).
% 67.57/68.02 cnf('1.0.0.1',plain,
% 67.57/68.02 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['1.0.0.0','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('L.2.2','L')]).
% 67.57/68.02 cnf('1.0.0.2',plain,
% 67.57/68.02 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,join(b,join(meet(b,c),meet(a,c)))))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['1.0.0.1','0.3897.2.0',theory(equality)]),
% 67.57/68.02 [pos('R','L')]).
% 67.57/68.02 cnf('1.0.0.3',plain,
% 67.57/68.02 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,join(meet(b,c),meet(a,c)))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['1.0.0.2','0.1815.2.0',theory(equality)]),
% 67.57/68.02 [pos('R.2','L')]).
% 67.57/68.02 cnf('1.0.0.4',plain,
% 67.57/68.02 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(a,c))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['1.0.0.3','0.17.2.0',theory(equality)]),
% 67.57/68.02 [pos('R.2','L')]).
% 67.57/68.02 cnf('1.0.0.5',plain,
% 67.57/68.02 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,a))) ),
% 67.57/68.02 inference(reduction,[status(thm)],['1.0.0.4','0.5.2.0',theory(equality)]),
% 67.57/68.02 [pos('R.2.2','L')]).
% 67.57/68.02 cnf('1.0.0.6',plain,
% 67.57/68.02 ( $true ),
% 67.57/68.02 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 67.57/68.02 [conjecture_1]).
% 67.57/68.02
% 67.57/68.02 Proved Goals:
% 67.57/68.02 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)))
% 67.57/68.02 1 goal was specified, which was proved.
% 67.57/68.02 % SZS output end CNFRefutation
% 67.57/68.02 #END OF PROOF
% 67.57/68.02
% 67.57/68.02 Problem WALDMEISTER_20173_n007
% 67.57/68.02 CPs.gen 15695179
% 67.57/68.02 CPs.reexp 0
% 67.57/68.02 Select 273378
% 67.57/68.02 R 3885
% 67.57/68.02 E 12
% 67.57/68.02 vsize 11.3M
% 67.57/68.02 rss 6.9M
% 67.57/68.02 process.time 67.036s
% 67.57/68.02 wallclock.time 67.036s
% 67.57/68.02 status S
% 67.57/68.02
% 67.57/68.02
% 67.57/68.02 Waldmeister states: Goal proved.
% 67.57/68.02 % SZS status Unsatisfiable
%------------------------------------------------------------------------------