TSTP Solution File: LAT022-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT022-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 07:14:47 EDT 2022
% Result : Unsatisfiable 1.00s 1.42s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : LAT022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.05/0.09 % Command : woody %s
% 0.08/0.29 % Computer : n008.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Wed Jun 29 00:08:53 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.55/0.94 ********************************************************************************
% 0.55/0.94 * W A L D M E I S T E R \| \ / \|/ *
% 0.55/0.94 * |/ | \/ | *
% 0.55/0.94 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.55/0.94 * A. Jaeger and B. Loechner | | *
% 0.55/0.94 * <waldmeister@informatik.uni-kl.de> | *
% 0.55/0.94 ********************************************************************************
% 0.55/0.94
% 0.55/0.94
% 0.55/0.94 Goals:
% 0.55/0.94 ------
% 0.55/0.94
% 0.55/0.94 ( 1) join(meet(a,b),meet(a,c)) ?=? meet(a,join(b,meet(a,c)))
% 0.55/0.94
% 0.55/0.94 Detected structure: Verband
% 0.55/0.94 ********************************************************************************
% 0.55/0.94 ****************************** COMPLETION - PROOF ******************************
% 0.55/0.94 ********************************************************************************
% 0.55/0.94
% 1.00/1.42 joined goal: 1 join(meet(a,b),meet(a,c)) ?= meet(a,join(b,meet(a,c))) to meet(a,join(b,meet(c,a)))
% 1.00/1.42 goal joined
% 1.00/1.42 % SZS status Unsatisfiable
% 1.00/1.42 #START OF PROOF
% 1.00/1.42 % SZS output start CNFRefutation
% 1.00/1.42 cnf('0.1.0.0',axiom,
% 1.00/1.42 ( X1 = join(X1,X1) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.1.1.0',plain,
% 1.00/1.42 ( X1 = join(X1,X1) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.00/1.42 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.00/1.42 cnf('0.1.2.0',plain,
% 1.00/1.42 ( join(X1,X1) = X1 ),
% 1.00/1.42 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_1]).
% 1.00/1.42 cnf('0.2.0.0',axiom,
% 1.00/1.42 ( X1 = meet(X1,X1) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.2.1.0',plain,
% 1.00/1.42 ( X1 = meet(X1,X1) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.00/1.42 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.00/1.42 cnf('0.2.2.0',plain,
% 1.00/1.42 ( meet(X1,X1) = X1 ),
% 1.00/1.42 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_2]).
% 1.00/1.42 cnf('0.3.0.0',axiom,
% 1.00/1.42 ( join(X1,X2) = join(X2,X1) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.3.1.0',plain,
% 1.00/1.42 ( join(X1,X2) = join(X2,X1) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.00/1.42 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.00/1.42 cnf('0.3.2.0',plain,
% 1.00/1.42 ( join(X1,X2) = join(X2,X1) ),
% 1.00/1.42 inference(activate,[status(thm)],['0.3.1.0']),
% 1.00/1.42 [equation_1]).
% 1.00/1.42 cnf('0.4.0.0',axiom,
% 1.00/1.42 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.4.1.0',plain,
% 1.00/1.42 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.00/1.42 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.00/1.42 cnf('0.4.2.0',plain,
% 1.00/1.42 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_3]).
% 1.00/1.42 cnf('0.5.0.0',axiom,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.5.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.00/1.42 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.00/1.42 cnf('0.5.2.0',plain,
% 1.00/1.42 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_4]).
% 1.00/1.42 cnf('0.6.0.0',axiom,
% 1.00/1.42 ( join(meet(X1,X2),meet(X3,join(X1,X2))) = meet(join(X1,X2),join(X3,meet(X1,X2))) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.6.1.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X3,join(X1,X2))) = meet(join(X1,X2),join(X3,meet(X1,X2))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.6.0.0']),
% 1.00/1.42 [weight('<5,0,0,[0,0,0,6]>')]).
% 1.00/1.42 cnf('0.6.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X3,join(X1,X2))) = meet(join(X1,X2),join(X3,meet(X1,X2))) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_5]).
% 1.00/1.42 cnf('0.7.0.0',axiom,
% 1.00/1.42 ( join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.7.1.0',plain,
% 1.00/1.42 ( join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.7.0.0']),
% 1.00/1.42 [weight('<6,0,0,[0,0,0,7]>')]).
% 1.00/1.42 cnf('0.7.1.1',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.7.1.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.7.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.7.1.1',theory(equality)]),
% 1.00/1.42 [u,rule_6]).
% 1.00/1.42 cnf('0.8.0.0',axiom,
% 1.00/1.42 ( meet(X1,X2) = meet(X2,X1) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.8.1.0',plain,
% 1.00/1.42 ( meet(X1,X2) = meet(X2,X1) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.8.0.0']),
% 1.00/1.42 [weight('<7,0,0,[0,0,0,8]>')]).
% 1.00/1.42 cnf('0.8.2.0',plain,
% 1.00/1.42 ( meet(X1,X2) = meet(X2,X1) ),
% 1.00/1.42 inference(activate,[status(thm)],['0.8.1.0']),
% 1.00/1.42 [equation_2]).
% 1.00/1.42 cnf('0.9.0.0',axiom,
% 1.00/1.42 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008')).
% 1.00/1.42 cnf('0.9.1.0',plain,
% 1.00/1.42 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.9.0.0']),
% 1.00/1.42 [weight('<8,0,0,[0,0,0,9]>')]).
% 1.00/1.42 cnf('0.9.2.0',plain,
% 1.00/1.42 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_7]).
% 1.00/1.42 cnf('0.10.0.0',plain,
% 1.00/1.42 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.4.2.0','0.1.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.10.1.0',plain,
% 1.00/1.42 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.10.0.0']),
% 1.00/1.42 [weight('<5,4,1,[1,0,0,1]>')]).
% 1.00/1.42 cnf('0.10.2.0',plain,
% 1.00/1.42 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_8]).
% 1.00/1.42 cnf('0.11.0.0',plain,
% 1.00/1.42 ( meet(join(X1,X1),join(X2,meet(X1,X1))) = join(meet(X1,X1),meet(X2,X1)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.6.2.0','0.1.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('0.11.0.1',plain,
% 1.00/1.42 ( meet(X1,join(X2,meet(X1,X1))) = join(meet(X1,X1),meet(X2,X1)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.11.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.11.0.2',plain,
% 1.00/1.42 ( meet(X1,join(X2,X1)) = join(meet(X1,X1),meet(X2,X1)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.11.0.1','0.2.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('0.11.0.3',plain,
% 1.00/1.42 ( meet(X1,join(X2,X1)) = join(X1,meet(X2,X1)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.11.0.2','0.2.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.1','L')]).
% 1.00/1.42 cnf('0.11.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X1)) = join(X1,meet(X2,X1)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.11.0.3']),
% 1.00/1.42 [weight('<5,6,1,[1,0,0,6]>')]).
% 1.00/1.42 cnf('0.11.2.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X1)) = meet(X1,join(X2,X1)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_9]).
% 1.00/1.42 cnf('0.12.0.0',plain,
% 1.00/1.42 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.9.2.0','0.2.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.12.1.0',plain,
% 1.00/1.42 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.12.0.0']),
% 1.00/1.42 [weight('<5,9,2,[1,0,0,1]>')]).
% 1.00/1.42 cnf('0.12.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_10]).
% 1.00/1.42 cnf('0.13.0.0',plain,
% 1.00/1.42 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.10.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.13.1.0',plain,
% 1.00/1.42 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.13.0.0']),
% 1.00/1.42 [weight('<5,10,3,[1,0,0,2]>')]).
% 1.00/1.42 cnf('0.13.2.0',plain,
% 1.00/1.42 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_11]).
% 1.00/1.42 cnf('0.14.0.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X1)) = join(X1,meet(X1,X2)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.11.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.14.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X1)) = join(X1,meet(X1,X2)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.14.0.0']),
% 1.00/1.42 [weight('<5,11,8,[1,0,0,2]>')]).
% 1.00/1.42 cnf('0.14.2.0',plain,
% 1.00/1.42 ( join(X1,meet(X1,X2)) = meet(X1,join(X2,X1)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_12]).
% 1.00/1.42 cnf('0.15.0.0',plain,
% 1.00/1.42 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.12.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.15.1.0',plain,
% 1.00/1.42 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.15.0.0']),
% 1.00/1.42 [weight('<5,12,8,[1,0,0,2]>')]).
% 1.00/1.42 cnf('0.15.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(X2,X1)) = meet(X1,X2) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_13]).
% 1.00/1.42 cnf('0.16.0.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X1),X3)) = join(meet(X1,join(X2,X1)),X3) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.4.2.0','0.11.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.16.1.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X1),X3)) = join(meet(X1,join(X2,X1)),X3) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.16.0.0']),
% 1.00/1.42 [weight('<7,11,4,[0,0,0,1]>')]).
% 1.00/1.42 cnf('0.16.2.0',plain,
% 1.00/1.42 ( join(meet(X1,join(X2,X1)),X3) = join(X1,join(meet(X2,X1),X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_14]).
% 1.00/1.42 cnf('0.18.0.0',plain,
% 1.00/1.42 ( join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.4.2.0','0.13.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.18.0.1',plain,
% 1.00/1.42 ( join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.18.0.0','0.4.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.18.0.2',plain,
% 1.00/1.42 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.18.0.1','0.4.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.18.1.0',plain,
% 1.00/1.42 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.18.0.2']),
% 1.00/1.42 [weight('<7,13,4,[0,0,0,1]>')]).
% 1.00/1.42 cnf('0.18.2.0',plain,
% 1.00/1.42 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_16]).
% 1.00/1.42 cnf('0.20.0.0',plain,
% 1.00/1.42 ( meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.9.2.0','0.15.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.20.0.1',plain,
% 1.00/1.42 ( meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.20.0.0','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.20.0.2',plain,
% 1.00/1.42 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.20.0.1','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.20.1.0',plain,
% 1.00/1.42 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.20.0.2']),
% 1.00/1.42 [weight('<7,15,9,[0,0,0,1]>')]).
% 1.00/1.42 cnf('0.20.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_18]).
% 1.00/1.42 cnf('0.23.0.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X1),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1.2','L')]).
% 1.00/1.42 cnf('0.23.1.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X1),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.23.0.0']),
% 1.00/1.42 [weight('<7,16,3,[1,0,0,3]>')]).
% 1.00/1.42 cnf('0.23.2.0',plain,
% 1.00/1.42 ( join(meet(X1,join(X1,X2)),X3) = join(X1,join(meet(X2,X1),X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_21]).
% 1.00/1.42 cnf('0.28.0.0',plain,
% 1.00/1.42 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 1.00/1.42 cnf('0.28.1.0',plain,
% 1.00/1.42 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.28.0.0']),
% 1.00/1.42 [weight('<9,5,8,[0,0,0,0]>')]).
% 1.00/1.42 cnf('0.28.1.1',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.28.1.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.28.2.0',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.28.1.1',theory(equality)]),
% 1.00/1.42 [u,rule_26]).
% 1.00/1.42 cnf('0.33.0.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.7.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('0.33.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.33.0.0']),
% 1.00/1.42 [weight('<9,7,3,[1,0,0,6]>')]).
% 1.00/1.42 cnf('0.33.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_31]).
% 1.00/1.42 cnf('0.34.0.0',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(X3,meet(X1,X2))) = join(meet(X1,X2),meet(join(X1,X2),X3)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.6.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.34.1.0',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(X3,meet(X1,X2))) = join(meet(X1,X2),meet(join(X1,X2),X3)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.34.0.0']),
% 1.00/1.42 [weight('<9,8,6,[0,0,0,4]>')]).
% 1.00/1.42 cnf('0.34.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(join(X1,X2),X3)) = meet(join(X1,X2),join(X3,meet(X1,X2))) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_32]).
% 1.00/1.42 cnf('0.37.0.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X2,X3))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.7.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.37.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X2,X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.37.0.0']),
% 1.00/1.42 [weight('<9,8,7,[0,0,0,1]>')]).
% 1.00/1.42 cnf('0.37.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_35]).
% 1.00/1.42 cnf('0.58.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,meet(X2,X3))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.28.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.58.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,meet(X2,X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.58.0.0']),
% 1.00/1.42 [weight('<9,28,3,[1,0,0,1]>')]).
% 1.00/1.42 cnf('0.58.2.0',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_56]).
% 1.00/1.42 cnf('0.71.0.0',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(meet(X1,join(X1,X2)),join(X1,meet(X2,X3))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.37.2.0','0.28.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.71.0.1',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(meet(X1,join(X1,X2)),join(X1,meet(X2,X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.71.0.0','0.28.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.71.0.2',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X1),join(X1,meet(X2,X3)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.71.0.1','0.23.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.71.0.3',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X1),meet(X2,X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.71.0.2','0.18.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.71.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X1),meet(X2,X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.71.0.3']),
% 1.00/1.42 [weight('<9,37,28,[1,0,0,4]>')]).
% 1.00/1.42 cnf('0.71.2.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X1),meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_69]).
% 1.00/1.42 cnf('0.84.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(meet(X2,X3),X1)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.58.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.84.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(meet(X2,X3),X1)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.84.0.0']),
% 1.00/1.42 [weight('<9,58,3,[1,0,0,4]>')]).
% 1.00/1.42 cnf('0.84.2.0',plain,
% 1.00/1.42 ( meet(join(X1,X2),join(meet(X1,X3),X2)) = join(X2,meet(X1,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.84.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_81]).
% 1.00/1.42 cnf('0.85.0.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(join(X1,meet(X1,X2)),meet(X1,join(X2,X3))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.58.2.0','0.7.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.85.0.1',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(join(X1,meet(X1,X2)),meet(X1,join(X2,X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.85.0.0','0.7.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.85.0.2',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(meet(X1,join(X2,X1)),meet(X1,join(X2,X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.85.0.1','0.14.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.1','L')]).
% 1.00/1.42 cnf('0.85.0.3',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X1),meet(X1,join(X2,X3)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.85.0.2','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.85.0.4',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X1),join(X2,X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.85.0.3','0.20.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.85.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X1),join(X2,X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.85.0.4']),
% 1.00/1.42 [weight('<9,58,7,[1,0,0,4]>')]).
% 1.00/1.42 cnf('0.85.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.85.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_82]).
% 1.00/1.42 cnf('0.94.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X3),meet(X2,X1))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.71.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.94.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X3),meet(X2,X1))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.94.0.0']),
% 1.00/1.42 [weight('<9,71,3,[1,0,0,2]>')]).
% 1.00/1.42 cnf('0.94.2.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X3),meet(X2,X1))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_91]).
% 1.00/1.42 cnf('0.102.0.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X1),join(X3,X2))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.85.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('0.102.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X1),join(X3,X2))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.102.0.0']),
% 1.00/1.42 [weight('<9,85,3,[1,0,0,6]>')]).
% 1.00/1.42 cnf('0.102.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X3,X2))) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_99]).
% 1.00/1.42 cnf('0.103.0.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X3),join(X2,X1))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.85.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.103.1.0',plain,
% 1.00/1.42 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X3),join(X2,X1))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.103.0.0']),
% 1.00/1.42 [weight('<9,85,8,[1,0,0,2]>')]).
% 1.00/1.42 cnf('0.103.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X3),join(X2,X1))) = meet(X1,join(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.103.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_100]).
% 1.00/1.42 cnf('0.114.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.94.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.1','L')]).
% 1.00/1.42 cnf('0.114.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.114.0.0']),
% 1.00/1.42 [weight('<9,94,8,[1,0,0,3]>')]).
% 1.00/1.42 cnf('0.114.2.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X3),meet(X3,X1))) = join(X1,meet(X3,X2)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.114.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_110]).
% 1.00/1.42 cnf('0.124.0.0',plain,
% 1.00/1.42 ( meet(meet(X1,X2),join(X3,X1)) = meet(meet(X1,X2),join(X3,meet(X1,X2))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.103.2.0','0.28.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.124.0.1',plain,
% 1.00/1.42 ( meet(X1,meet(X2,join(X3,X1))) = meet(meet(X1,X2),join(X3,meet(X1,X2))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.124.0.0','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.124.0.2',plain,
% 1.00/1.42 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.124.0.1','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.124.1.0',plain,
% 1.00/1.42 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.124.0.2']),
% 1.00/1.42 [weight('<9,103,28,[1,0,0,2]>')]).
% 1.00/1.42 cnf('0.124.2.0',plain,
% 1.00/1.42 ( meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,meet(X2,join(X3,X1))) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_119]).
% 1.00/1.42 cnf('0.141.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X3,X2),meet(X1,X2))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.114.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('0.141.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X3,X2),meet(X1,X2))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.141.0.0']),
% 1.00/1.42 [weight('<9,114,8,[1,0,0,6]>')]).
% 1.00/1.42 cnf('0.141.2.0',plain,
% 1.00/1.42 ( join(X1,join(meet(X2,X3),meet(X1,X3))) = join(X1,meet(X3,X2)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.141.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_133]).
% 1.00/1.42 cnf('0.175.0.0',plain,
% 1.00/1.42 ( join(X1,meet(meet(X2,X3),X2)) = join(X1,join(meet(X2,X3),meet(X1,meet(X2,X3)))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.141.2.0','0.12.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.1','L')]).
% 1.00/1.42 cnf('0.175.0.1',plain,
% 1.00/1.42 ( join(X1,meet(X2,meet(X3,X2))) = join(X1,join(meet(X2,X3),meet(X1,meet(X2,X3)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.175.0.0','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.175.0.2',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X3),meet(X1,meet(X2,X3)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.175.0.1','0.15.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.175.0.3',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(meet(X2,X3),join(X1,meet(X2,X3)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.175.0.2','0.11.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.2','L')]).
% 1.00/1.42 cnf('0.175.0.4',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,meet(X3,join(X1,meet(X2,X3))))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.175.0.3','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.2','L')]).
% 1.00/1.42 cnf('0.175.0.5',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,meet(X3,join(X1,X2)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.175.0.4','0.124.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.2','L')]).
% 1.00/1.42 cnf('0.175.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,meet(X3,join(X1,X2)))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.175.0.5']),
% 1.00/1.42 [weight('<9,141,12,[1,0,0,3]>')]).
% 1.00/1.42 cnf('0.175.2.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,meet(X3,join(X1,X2)))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.175.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_162]).
% 1.00/1.42 cnf('0.227.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,meet(join(X1,X2),X3))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.175.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('0.227.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,meet(join(X1,X2),X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.227.0.0']),
% 1.00/1.42 [weight('<9,175,8,[1,0,0,4]>')]).
% 1.00/1.42 cnf('0.227.2.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,meet(join(X1,X2),X3))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.227.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_210]).
% 1.00/1.42 cnf('0.307.0.0',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,join(X3,meet(X1,X2)))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.33.2.0','0.12.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.307.1.0',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,join(X3,meet(X1,X2)))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.307.0.0']),
% 1.00/1.42 [weight('<11,33,12,[1,0,0,1]>')]).
% 1.00/1.42 cnf('0.307.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,join(X3,meet(X1,X2)))) = meet(X1,join(meet(X1,X2),X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.307.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_283]).
% 1.00/1.42 cnf('0.310.0.0',plain,
% 1.00/1.42 ( meet(join(X1,meet(X2,X1)),join(X3,meet(X1,meet(X2,X1)))) = join(meet(X1,meet(X2,X1)),meet(meet(X1,join(X2,X1)),X3)) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.34.2.0','0.11.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.1','L')]).
% 1.00/1.42 cnf('0.310.0.1',plain,
% 1.00/1.42 ( meet(meet(X1,join(X2,X1)),join(X3,meet(X1,meet(X2,X1)))) = join(meet(X1,meet(X2,X1)),meet(meet(X1,join(X2,X1)),X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.310.0.0','0.11.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.1','L')]).
% 1.00/1.42 cnf('0.310.0.2',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X3,meet(X1,meet(X2,X1))))) = join(meet(X1,meet(X2,X1)),meet(meet(X1,join(X2,X1)),X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.310.0.1','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.310.0.3',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X3,meet(X1,X2)))) = join(meet(X1,meet(X2,X1)),meet(meet(X1,join(X2,X1)),X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.310.0.2','0.15.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2.2','L')]).
% 1.00/1.42 cnf('0.310.0.4',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X3,meet(X1,X2)))) = join(meet(X1,X2),meet(meet(X1,join(X2,X1)),X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.310.0.3','0.15.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.1','L')]).
% 1.00/1.42 cnf('0.310.0.5',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X3,meet(X1,X2)))) = join(meet(X1,X2),meet(X1,meet(join(X2,X1),X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.310.0.4','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.2','L')]).
% 1.00/1.42 cnf('0.310.1.0',plain,
% 1.00/1.42 ( meet(X1,meet(join(X2,X1),join(X3,meet(X1,X2)))) = join(meet(X1,X2),meet(X1,meet(join(X2,X1),X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.310.0.5']),
% 1.00/1.42 [weight('<11,34,11,[1,0,0,5]>')]).
% 1.00/1.42 cnf('0.310.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,meet(join(X2,X1),X3))) = meet(X1,meet(join(X2,X1),join(X3,meet(X1,X2)))) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.310.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_286]).
% 1.00/1.42 cnf('0.311.0.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,meet(join(X1,X2),X3))) = join(X1,meet(X2,meet(join(X1,X2),join(X3,meet(X2,X1))))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.71.2.0','0.310.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.311.0.1',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,meet(join(X1,X2),join(X3,meet(X2,X1))))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.311.0.0','0.227.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.311.0.2',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.311.0.1','0.227.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.311.1.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,X3)) = join(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.311.0.2']),
% 1.00/1.42 [weight('<9,310,71,[0,0,0,2]>')]).
% 1.00/1.42 cnf('0.311.2.0',plain,
% 1.00/1.42 ( join(X1,meet(X2,join(X3,meet(X2,X1)))) = join(X1,meet(X2,X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.311.1.0',theory(equality)]),
% 1.00/1.42 [x,rule_287]).
% 1.00/1.42 cnf('0.312.0.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,X3)) = join(meet(X1,X2),meet(X1,join(X3,meet(X1,X2)))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.311.2.0','0.12.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2.2','L')]).
% 1.00/1.42 cnf('0.312.0.1',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),X3)) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.312.0.0','0.307.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.312.1.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),X3)) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.312.0.1']),
% 1.00/1.42 [weight('<7,311,12,[1,0,0,6]>')]).
% 1.00/1.42 cnf('0.312.2.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),X3)) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.312.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_288]).
% 1.00/1.42 cnf('0.315.0.0',plain,
% 1.00/1.42 ( join(meet(X1,X2),meet(X1,X3)) = meet(join(X1,meet(X1,X2)),meet(X1,join(meet(X1,X3),X2))) ),
% 1.00/1.42 inference(cp,[status(thm)],['0.84.2.0','0.312.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2','L')]).
% 1.00/1.42 cnf('0.315.0.1',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(join(X1,meet(X1,X2)),meet(X1,join(meet(X1,X3),X2))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.315.0.0','0.312.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('0.315.0.2',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(meet(X1,join(X2,X1)),meet(X1,join(meet(X1,X3),X2))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.315.0.1','0.14.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.1','L')]).
% 1.00/1.42 cnf('0.315.0.3',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,meet(join(X2,X1),meet(X1,join(meet(X1,X3),X2)))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.315.0.2','0.9.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.315.0.4',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,meet(join(X2,X1),join(meet(X1,X3),X2))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.315.0.3','0.20.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.315.0.5',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['0.315.0.4','0.102.2.0',theory(equality)]),
% 1.00/1.42 [pos('R','L')]).
% 1.00/1.42 cnf('0.315.1.0',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 1.00/1.42 inference(weigh,[status(thm)],['0.315.0.5']),
% 1.00/1.42 [weight('<7,312,84,[0,0,0,4]>')]).
% 1.00/1.42 cnf('0.315.2.0',plain,
% 1.00/1.42 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 1.00/1.42 inference(orient,[status(thm)],['0.315.1.0',theory(equality)]),
% 1.00/1.42 [u,rule_291]).
% 1.00/1.42 cnf('1.0.0.0',conjecture,
% 1.00/1.42 ( join(meet(a,b),meet(a,c)) = meet(a,join(b,meet(a,c))) ),
% 1.00/1.42 file('/tmp/WALDMEISTER_6551_n008',conjecture_1)).
% 1.00/1.42 cnf('1.0.0.1',plain,
% 1.00/1.42 ( meet(a,join(meet(a,b),c)) = meet(a,join(b,meet(a,c))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['1.0.0.0','0.312.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('1.0.0.2',plain,
% 1.00/1.42 ( meet(a,join(b,meet(a,c))) = meet(a,join(b,meet(a,c))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['1.0.0.1','0.315.2.0',theory(equality)]),
% 1.00/1.42 [pos('L','L')]).
% 1.00/1.42 cnf('1.0.0.3',plain,
% 1.00/1.42 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(a,c))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['1.0.0.2','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('L.2.2','L')]).
% 1.00/1.42 cnf('1.0.0.4',plain,
% 1.00/1.42 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,a))) ),
% 1.00/1.42 inference(reduction,[status(thm)],['1.0.0.3','0.8.2.0',theory(equality)]),
% 1.00/1.42 [pos('R.2.2','L')]).
% 1.00/1.42 cnf('1.0.0.5',plain,
% 1.00/1.42 ( $true ),
% 1.00/1.42 inference(trivial,[status(thm)],['1.0.0.4',theory(equality)]),
% 1.00/1.42 [conjecture_1]).
% 1.00/1.42
% 1.00/1.42 Proved Goals:
% 1.00/1.42 No. 1: join(meet(a,b),meet(a,c)) ?= meet(a,join(b,meet(a,c))) joined, current: meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,a)))
% 1.00/1.42 1 goal was specified, which was proved.
% 1.00/1.42 % SZS output end CNFRefutation
% 1.00/1.42 #END OF PROOF
% 1.00/1.42
% 1.00/1.42 Problem WALDMEISTER_6551_n008
% 1.00/1.42 CPs.gen 68220
% 1.00/1.42 CPs.reexp 0
% 1.00/1.42 Select 3079
% 1.00/1.42 R 291
% 1.00/1.42 E 24
% 1.00/1.42 vsize 6.5M
% 1.00/1.42 rss 3.8M
% 1.00/1.42 process.time 0.484s
% 1.00/1.42 wallclock.time 0.484s
% 1.00/1.42 status S
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 Waldmeister states: Goal proved.
% 1.00/1.42 % SZS status Unsatisfiable
%------------------------------------------------------------------------------