TSTP Solution File: LAT172-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT172-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n005.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 07:15:30 EDT 2022
% Result : Unsatisfiable 52.06s 52.44s
% Output : CNFRefutation 52.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT172-1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n005.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 : Tue Jun 28 22:33:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.62/0.98 ********************************************************************************
% 0.62/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/0.98 * |/ | \/ | *
% 0.62/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/0.98 * A. Jaeger and B. Loechner | | *
% 0.62/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/0.98 ********************************************************************************
% 0.62/0.98
% 0.62/0.98
% 0.62/0.98 Goals:
% 0.62/0.98 ------
% 0.62/0.98
% 0.62/0.98 ( 1) meet(a,join(b,meet(c,join(meet(a,d),meet(b,d))))) ?=? meet(a,join(b,meet(a,meet(c,d))))
% 0.62/0.98
% 0.62/0.98 Detected structure: Verband
% 0.62/0.98 ********************************************************************************
% 0.62/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.62/0.98 ********************************************************************************
% 0.62/0.98
% 52.06/52.44 joined goal: 1 meet(a,join(b,meet(c,join(meet(a,d),meet(b,d))))) ?= meet(a,join(b,meet(a,meet(c,d)))) to meet(a,join(b,meet(d,meet(a,c))))
% 52.06/52.44 goal joined
% 52.06/52.44 % SZS status Unsatisfiable
% 52.06/52.44 #START OF PROOF
% 52.06/52.44 % SZS output start CNFRefutation
% 52.06/52.44 cnf('0.1.0.0',axiom,
% 52.06/52.44 ( X1 = join(X1,X1) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.1.1.0',plain,
% 52.06/52.44 ( X1 = join(X1,X1) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.1.0.0']),
% 52.06/52.44 [weight('<0,0,0,[0,0,0,1]>')]).
% 52.06/52.44 cnf('0.1.2.0',plain,
% 52.06/52.44 ( join(X1,X1) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_1]).
% 52.06/52.44 cnf('0.2.0.0',axiom,
% 52.06/52.44 ( X1 = join(X1,meet(X1,X2)) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.2.1.0',plain,
% 52.06/52.44 ( X1 = join(X1,meet(X1,X2)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.2.0.0']),
% 52.06/52.44 [weight('<1,0,0,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.2.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X1,X2)) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_2]).
% 52.06/52.44 cnf('0.3.0.0',axiom,
% 52.06/52.44 ( X1 = meet(X1,X1) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.3.1.0',plain,
% 52.06/52.44 ( X1 = meet(X1,X1) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.3.0.0']),
% 52.06/52.44 [weight('<2,0,0,[0,0,0,3]>')]).
% 52.06/52.44 cnf('0.3.2.0',plain,
% 52.06/52.44 ( meet(X1,X1) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_3]).
% 52.06/52.44 cnf('0.4.0.0',axiom,
% 52.06/52.44 ( X1 = meet(X1,join(X1,X2)) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.4.1.0',plain,
% 52.06/52.44 ( X1 = meet(X1,join(X1,X2)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.4.0.0']),
% 52.06/52.44 [weight('<3,0,0,[0,0,0,4]>')]).
% 52.06/52.44 cnf('0.4.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X1,X2)) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_4]).
% 52.06/52.44 cnf('0.5.0.0',axiom,
% 52.06/52.44 ( join(X1,X2) = join(X2,X1) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.5.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X2,X1) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.5.0.0']),
% 52.06/52.44 [weight('<4,0,0,[0,0,0,5]>')]).
% 52.06/52.44 cnf('0.5.2.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X2,X1) ),
% 52.06/52.44 inference(activate,[status(thm)],['0.5.1.0']),
% 52.06/52.44 [equation_1]).
% 52.06/52.44 cnf('0.6.0.0',axiom,
% 52.06/52.44 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.6.1.0',plain,
% 52.06/52.44 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.6.0.0']),
% 52.06/52.44 [weight('<5,0,0,[0,0,0,6]>')]).
% 52.06/52.44 cnf('0.6.2.0',plain,
% 52.06/52.44 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_5]).
% 52.06/52.44 cnf('0.7.0.0',axiom,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,X4)))) = join(X1,meet(X2,join(X3,meet(X4,join(X1,X2))))) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.7.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,X4)))) = join(X1,meet(X2,join(X3,meet(X4,join(X1,X2))))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.7.0.0']),
% 52.06/52.44 [weight('<6,0,0,[0,0,0,7]>')]).
% 52.06/52.44 cnf('0.7.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X4,join(X1,X2))))) = join(X1,meet(X2,join(X3,meet(X2,X4)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_6]).
% 52.06/52.44 cnf('0.8.0.0',axiom,
% 52.06/52.44 ( meet(X1,X2) = meet(X2,X1) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.8.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X2,X1) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.8.0.0']),
% 52.06/52.44 [weight('<7,0,0,[0,0,0,8]>')]).
% 52.06/52.44 cnf('0.8.2.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X2,X1) ),
% 52.06/52.44 inference(activate,[status(thm)],['0.8.1.0']),
% 52.06/52.44 [equation_2]).
% 52.06/52.44 cnf('0.9.0.0',axiom,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005')).
% 52.06/52.44 cnf('0.9.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.9.0.0']),
% 52.06/52.44 [weight('<8,0,0,[0,0,0,9]>')]).
% 52.06/52.44 cnf('0.9.2.0',plain,
% 52.06/52.44 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_7]).
% 52.06/52.44 cnf('0.10.0.0',plain,
% 52.06/52.44 ( X1 = meet(X1,join(X2,X1)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.10.1.0',plain,
% 52.06/52.44 ( X1 = meet(X1,join(X2,X1)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.10.0.0']),
% 52.06/52.44 [weight('<5,5,4,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.10.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,X1)) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_8]).
% 52.06/52.44 cnf('0.11.0.0',plain,
% 52.06/52.44 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.6.2.0','0.1.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.11.1.0',plain,
% 52.06/52.44 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.11.0.0']),
% 52.06/52.44 [weight('<5,6,1,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.11.2.0',plain,
% 52.06/52.44 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_9]).
% 52.06/52.44 cnf('0.12.0.0',plain,
% 52.06/52.44 ( X1 = join(X1,meet(X2,X1)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.2.2.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.12.1.0',plain,
% 52.06/52.44 ( X1 = join(X1,meet(X2,X1)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.12.0.0']),
% 52.06/52.44 [weight('<5,8,2,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.12.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,X1)) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_10]).
% 52.06/52.44 cnf('0.13.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.9.2.0','0.3.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.13.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.13.0.0']),
% 52.06/52.44 [weight('<5,9,3,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.13.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_11]).
% 52.06/52.44 cnf('0.14.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(meet(X1,X2),X1) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.10.2.0','0.2.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.14.0.1',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.14.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.14.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.14.0.1']),
% 52.06/52.44 [weight('<5,10,2,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.14.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X1)) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_12]).
% 52.06/52.44 cnf('0.15.0.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.11.2.0','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.15.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.15.0.0']),
% 52.06/52.44 [weight('<5,11,5,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.15.2.0',plain,
% 52.06/52.44 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_13]).
% 52.06/52.44 cnf('0.16.0.0',plain,
% 52.06/52.44 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.16.1.0',plain,
% 52.06/52.44 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.16.0.0']),
% 52.06/52.44 [weight('<7,6,2,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.16.2.0',plain,
% 52.06/52.44 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_14]).
% 52.06/52.44 cnf('0.17.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.17.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.17.0.0']),
% 52.06/52.44 [weight('<7,9,4,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.17.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_15]).
% 52.06/52.44 cnf('0.18.0.0',plain,
% 52.06/52.44 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.10.2.0','0.6.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.18.1.0',plain,
% 52.06/52.44 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.18.0.0']),
% 52.06/52.44 [weight('<7,10,6,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.18.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,join(X3,X1))) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_16]).
% 52.06/52.44 cnf('0.20.0.0',plain,
% 52.06/52.44 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.6.2.0','0.12.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.20.1.0',plain,
% 52.06/52.44 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.20.0.0']),
% 52.06/52.44 [weight('<7,12,6,[0,0,0,1]>')]).
% 52.06/52.44 cnf('0.20.2.0',plain,
% 52.06/52.44 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_18]).
% 52.06/52.44 cnf('0.22.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.9.2.0','0.14.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.22.0.1',plain,
% 52.06/52.44 ( meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.22.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.22.0.2',plain,
% 52.06/52.44 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.22.0.1','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.22.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.22.0.2']),
% 52.06/52.44 [weight('<7,14,9,[0,0,0,1]>')]).
% 52.06/52.44 cnf('0.22.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_20]).
% 52.06/52.44 cnf('0.23.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(X1,meet(X2,meet(X3,X1))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.14.2.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.23.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(X1,meet(X2,meet(X3,X1))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.23.0.0']),
% 52.06/52.44 [weight('<7,14,9,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.23.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,meet(X3,X1))) = meet(X1,meet(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_21]).
% 52.06/52.44 cnf('0.25.0.0',plain,
% 52.06/52.44 ( join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.6.2.0','0.15.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.25.0.1',plain,
% 52.06/52.44 ( join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.25.0.0','0.6.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.25.0.2',plain,
% 52.06/52.44 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.25.0.1','0.6.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.25.1.0',plain,
% 52.06/52.44 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.25.0.2']),
% 52.06/52.44 [weight('<7,15,6,[0,0,0,1]>')]).
% 52.06/52.44 cnf('0.25.2.0',plain,
% 52.06/52.44 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_23]).
% 52.06/52.44 cnf('0.29.0.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X1,X3))) = join(X1,meet(X1,X3)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.16.2.0','0.12.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.29.0.1',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X1,X3))) = X1 ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.29.0.0','0.2.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.29.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X1,X3))) = X1 ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.29.0.1']),
% 52.06/52.44 [weight('<7,16,12,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.29.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X1,X3))) = X1 ),
% 52.06/52.44 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_27]).
% 52.06/52.44 cnf('0.30.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.17.2.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.30.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.30.0.0']),
% 52.06/52.44 [weight('<7,17,8,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.30.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_28]).
% 52.06/52.44 cnf('0.36.0.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,X1)))) = join(X1,meet(X2,join(X3,X1))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.7.2.0','0.4.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.36.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,X1)))) = join(X1,meet(X2,join(X3,X1))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.36.0.0']),
% 52.06/52.44 [weight('<9,7,4,[1,0,0,6]>')]).
% 52.06/52.44 cnf('0.36.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,X1)))) = join(X1,meet(X2,join(X3,X1))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_34]).
% 52.06/52.44 cnf('0.38.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.38.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.38.0.0']),
% 52.06/52.44 [weight('<9,9,4,[1,0,0,0]>')]).
% 52.06/52.44 cnf('0.38.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_36]).
% 52.06/52.44 cnf('0.39.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.10.2.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.39.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.39.0.0']),
% 52.06/52.44 [weight('<9,10,9,[1,0,0,0]>')]).
% 52.06/52.44 cnf('0.39.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_37]).
% 52.06/52.44 cnf('0.40.0.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.40.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.40.0.0']),
% 52.06/52.44 [weight('<9,12,6,[1,0,0,0]>')]).
% 52.06/52.44 cnf('0.40.2.0',plain,
% 52.06/52.44 ( join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_38]).
% 52.06/52.44 cnf('0.41.0.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.10.2.0','0.16.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.41.1.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.41.0.0']),
% 52.06/52.44 [weight('<9,16,10,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.41.1.1',plain,
% 52.06/52.44 ( join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.41.1.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.41.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.41.1.1',theory(equality)]),
% 52.06/52.44 [x,rule_39]).
% 52.06/52.44 cnf('0.42.0.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),join(X1,X3)) = meet(join(X1,X3),join(meet(X1,X2),join(X1,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.41.2.0','0.11.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.42.0.1',plain,
% 52.06/52.44 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.42.0.0','0.10.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.42.1.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.42.0.1']),
% 52.06/52.44 [weight('<7,41,11,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.42.2.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_40]).
% 52.06/52.44 cnf('0.44.0.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(meet(X3,X1),join(X1,X2)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.42.2.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.44.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(meet(X3,X1),join(X1,X2)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.44.0.0']),
% 52.06/52.44 [weight('<7,42,8,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.44.2.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),join(X2,X3)) = join(X2,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_42]).
% 52.06/52.44 cnf('0.46.0.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.12.2.0','0.17.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.46.1.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.46.0.0']),
% 52.06/52.44 [weight('<9,17,12,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.46.1.1',plain,
% 52.06/52.44 ( meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.46.1.0','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.46.2.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.46.1.1',theory(equality)]),
% 52.06/52.44 [x,rule_44]).
% 52.06/52.44 cnf('0.47.0.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X1,X3)) = join(meet(X1,X3),meet(join(X1,X2),meet(X1,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.46.2.0','0.13.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.47.0.1',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.47.0.0','0.12.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.47.1.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.47.0.1']),
% 52.06/52.44 [weight('<7,46,13,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.47.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_45]).
% 52.06/52.44 cnf('0.49.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(join(X1,X3),meet(X2,X1)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.47.2.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.49.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(join(X1,X3),meet(X2,X1)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.49.0.0']),
% 52.06/52.44 [weight('<7,47,8,[1,0,0,4]>')]).
% 52.06/52.44 cnf('0.49.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,X1)) = meet(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_47]).
% 52.06/52.44 cnf('0.52.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X2,join(X3,X1)),X4)) = meet(X1,X4) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.9.2.0','0.18.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.52.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X2,join(X3,X1)),X4)) = meet(X1,X4) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.52.0.0']),
% 52.06/52.44 [weight('<9,18,9,[0,0,0,1]>')]).
% 52.06/52.44 cnf('0.52.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X2,join(X3,X1)),X4)) = meet(X1,X4) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_50]).
% 52.06/52.44 cnf('0.59.0.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.10.2.0','0.20.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.59.1.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.59.0.0']),
% 52.06/52.44 [weight('<9,20,10,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.59.1.1',plain,
% 52.06/52.44 ( join(meet(X1,X2),X3) = meet(join(X2,X3),join(meet(X1,X2),X3)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.59.1.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.59.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),join(meet(X3,X1),X2)) = join(meet(X3,X1),X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.59.1.1',theory(equality)]),
% 52.06/52.44 [x,rule_57]).
% 52.06/52.44 cnf('0.76.0.0',plain,
% 52.06/52.44 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.18.2.0','0.25.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.76.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.76.0.0']),
% 52.06/52.44 [weight('<9,25,18,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.76.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_74]).
% 52.06/52.44 cnf('0.97.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.39.2.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.97.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.97.0.0']),
% 52.06/52.44 [weight('<9,39,8,[1,0,0,6]>')]).
% 52.06/52.44 cnf('0.97.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.97.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_95]).
% 52.06/52.44 cnf('0.98.0.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.40.2.0','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.98.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X2,X1)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.98.0.0']),
% 52.06/52.44 [weight('<9,40,5,[1,0,0,6]>')]).
% 52.06/52.44 cnf('0.98.2.0',plain,
% 52.06/52.44 ( join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_96]).
% 52.06/52.44 cnf('0.109.0.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.46.2.0','0.4.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.109.1.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.109.0.0']),
% 52.06/52.44 [weight('<9,46,4,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.109.2.0',plain,
% 52.06/52.44 ( join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_107]).
% 52.06/52.44 cnf('0.112.0.0',plain,
% 52.06/52.44 ( meet(meet(X1,X2),X3) = meet(join(X2,X4),meet(meet(X1,X2),X3)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.47.2.0','0.44.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.112.0.1',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X2,X4),meet(meet(X1,X2),X3)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.112.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.112.0.2',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X2,X4),meet(X1,meet(X2,X3))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.112.0.1','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('R.2','L')]).
% 52.06/52.44 cnf('0.112.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X2,X4),meet(X1,meet(X2,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.112.0.2']),
% 52.06/52.44 [weight('<9,47,44,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.112.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,meet(X1,X4))) = meet(X3,meet(X1,X4)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.112.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_110]).
% 52.06/52.44 cnf('0.115.0.0',plain,
% 52.06/52.44 ( meet(meet(X1,X2),X3) = meet(join(X1,X4),meet(X3,meet(X1,X2))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.49.2.0','0.42.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.115.0.1',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X1,X4),meet(X3,meet(X1,X2))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.115.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.115.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X1,X4),meet(X3,meet(X1,X2))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.115.0.1']),
% 52.06/52.44 [weight('<9,49,42,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.115.1.1',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.115.1.0','0.112.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.115.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 52.06/52.44 inference(activate,[status(thm)],['0.115.1.1']),
% 52.06/52.44 [equation_4]).
% 52.06/52.44 cnf('0.119.0.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),meet(X2,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.59.2.0','0.2.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.119.1.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),meet(X2,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.119.0.0']),
% 52.06/52.44 [weight('<9,59,2,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.119.2.0',plain,
% 52.06/52.44 ( meet(X1,join(meet(X2,X1),meet(X1,X3))) = join(meet(X2,X1),meet(X1,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.119.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_115]).
% 52.06/52.44 cnf('0.121.0.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),meet(X3,X2))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.59.2.0','0.12.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.121.1.0',plain,
% 52.06/52.44 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),meet(X3,X2))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.121.0.0']),
% 52.06/52.44 [weight('<9,59,12,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.121.2.0',plain,
% 52.06/52.44 ( meet(X1,join(meet(X2,X1),meet(X3,X1))) = join(meet(X2,X1),meet(X3,X1)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.121.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_117]).
% 52.06/52.44 cnf('0.125.0.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.76.2.0','0.2.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.125.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.125.0.0']),
% 52.06/52.44 [weight('<9,76,2,[1,0,0,6]>')]).
% 52.06/52.44 cnf('0.125.1.1',plain,
% 52.06/52.44 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,meet(X2,X3))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.125.1.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.125.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.125.1.1',theory(equality)]),
% 52.06/52.44 [x,rule_121]).
% 52.06/52.44 cnf('0.133.0.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,meet(join(X2,X3),join(X2,X1))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.98.2.0','0.109.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.133.1.0',plain,
% 52.06/52.44 ( join(X1,X2) = join(X1,meet(join(X2,X3),join(X2,X1))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.133.0.0']),
% 52.06/52.44 [weight('<9,109,98,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.133.2.0',plain,
% 52.06/52.44 ( join(X1,meet(join(X2,X3),join(X2,X1))) = join(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_128]).
% 52.06/52.44 cnf('0.134.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X4,X2),meet(X1,meet(X2,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.112.2.0','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.1','L')]).
% 52.06/52.44 cnf('0.134.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(join(X4,X2),meet(X1,meet(X2,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.134.0.0']),
% 52.06/52.44 [weight('<9,112,5,[1,0,0,1]>')]).
% 52.06/52.44 cnf('0.134.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,meet(X2,X4))) = meet(X3,meet(X2,X4)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_129]).
% 52.06/52.44 cnf('0.136.0.0',plain,
% 52.06/52.44 ( meet(meet(X1,join(X2,X3)),meet(X4,X2)) = meet(X4,meet(X2,X1)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.115.2.0','0.30.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.136.0.1',plain,
% 52.06/52.44 ( meet(X1,meet(join(X2,X3),meet(X4,X2))) = meet(X4,meet(X2,X1)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.136.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.136.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(join(X2,X3),meet(X4,X2))) = meet(X4,meet(X2,X1)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.136.0.1']),
% 52.06/52.44 [weight('<9,115,30,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.136.1.1',plain,
% 52.06/52.44 ( meet(X1,meet(X2,meet(join(X2,X3),X4))) = meet(X4,meet(X2,X1)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.136.1.0','0.115.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.136.1.2',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X4)) = meet(X4,meet(X2,X1)) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.136.1.1','0.17.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.136.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)) ),
% 52.06/52.44 inference(activate,[status(thm)],['0.136.1.2']),
% 52.06/52.44 [equation_6]).
% 52.06/52.44 cnf('0.142.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(X2,X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.38.2.0','0.119.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.142.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(X2,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.142.0.0']),
% 52.06/52.44 [weight('<9,119,38,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.142.2.0',plain,
% 52.06/52.44 ( meet(X1,join(meet(X1,X2),meet(X2,X3))) = meet(X1,X2) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_136]).
% 52.06/52.44 cnf('0.143.0.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.97.2.0','0.119.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.143.1.0',plain,
% 52.06/52.44 ( meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.143.0.0']),
% 52.06/52.44 [weight('<9,119,97,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.143.2.0',plain,
% 52.06/52.44 ( meet(X1,join(meet(X2,X3),meet(X3,X1))) = meet(X1,X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.143.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_137]).
% 52.06/52.44 cnf('0.154.0.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,X3)) = meet(X1,join(meet(X1,join(X2,X3)),X2)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.142.2.0','0.133.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.154.1.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,X3)) = meet(X1,join(meet(X1,join(X2,X3)),X2)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.154.0.0']),
% 52.06/52.44 [weight('<9,142,133,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.154.1.1',plain,
% 52.06/52.44 ( meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(X2,X3)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.154.1.0','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('R.2','L')]).
% 52.06/52.44 cnf('0.154.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X1,join(X2,X3)))) = meet(X1,join(X2,X3)) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.154.1.1',theory(equality)]),
% 52.06/52.44 [x,rule_148]).
% 52.06/52.44 cnf('0.156.0.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X1,join(X2,meet(X1,X3))))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.154.2.0','0.7.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.156.0.1',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X1,X3))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.156.0.0','0.154.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.156.1.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X1,X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.156.0.1']),
% 52.06/52.44 [weight('<9,154,7,[1,0,0,2]>')]).
% 52.06/52.44 cnf('0.156.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X1,X3))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.156.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_150]).
% 52.06/52.44 cnf('0.158.0.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(join(X2,X1),X3))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.156.2.0','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.158.1.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(join(X2,X1),X3))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.158.0.0']),
% 52.06/52.44 [weight('<9,156,8,[1,0,0,4]>')]).
% 52.06/52.44 cnf('0.158.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(join(X2,X1),X3))) = meet(X1,join(X2,meet(X1,X3))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.158.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_152]).
% 52.06/52.44 cnf('0.209.0.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,meet(X1,X4))))) = join(X1,join(meet(X1,X4),meet(X2,join(X3,meet(X1,X4))))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.16.2.0','0.36.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.209.0.1',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,meet(X1,X4))))) = join(X1,meet(X2,join(X3,meet(X1,X4)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.209.0.0','0.16.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.209.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,meet(X1,X4))))) = join(X1,meet(X2,join(X3,meet(X1,X4)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.209.0.1']),
% 52.06/52.44 [weight('<11,36,16,[0,0,0,2]>')]).
% 52.06/52.44 cnf('0.209.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X2,meet(X1,X4))))) = join(X1,meet(X2,join(X3,meet(X1,X4)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.209.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_201]).
% 52.06/52.44 cnf('0.244.0.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),X3) = meet(join(X1,X2),meet(join(X1,join(X4,X2)),X3)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.52.2.0','0.25.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.1','L')]).
% 52.06/52.44 cnf('0.244.1.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),X3) = meet(join(X1,X2),meet(join(X1,join(X4,X2)),X3)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.244.0.0']),
% 52.06/52.44 [weight('<11,52,25,[1,0,0,3]>')]).
% 52.06/52.44 cnf('0.244.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(join(X1,join(X3,X2)),X4)) = meet(join(X1,X2),X4) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.244.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_236]).
% 52.06/52.44 cnf('0.491.0.0',plain,
% 52.06/52.44 ( meet(join(X1,meet(X2,X3)),meet(X4,join(X1,X2))) = meet(join(X1,meet(X2,X3)),meet(X4,join(X1,meet(X2,X3)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.23.2.0','0.125.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.491.0.1',plain,
% 52.06/52.44 ( meet(join(X1,meet(X2,X3)),meet(X4,join(X1,X2))) = meet(join(X1,meet(X2,X3)),X4) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.491.0.0','0.14.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.491.1.0',plain,
% 52.06/52.44 ( meet(join(X1,meet(X2,X3)),meet(X4,join(X1,X2))) = meet(join(X1,meet(X2,X3)),X4) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.491.0.1']),
% 52.06/52.44 [weight('<11,125,23,[0,0,0,4]>')]).
% 52.06/52.44 cnf('0.491.1.1',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X4,join(X1,meet(X2,X3)))) = meet(join(X1,meet(X2,X3)),X4) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.491.1.0','0.136.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.491.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(X2,X4)))) = meet(join(X1,meet(X2,X4)),X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.491.1.1',theory(equality)]),
% 52.06/52.44 [u,rule_483]).
% 52.06/52.44 cnf('0.617.0.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X1,meet(X3,X4)))) = meet(X1,join(X2,meet(X3,meet(X4,join(X2,X1))))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.156.2.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.617.1.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X1,meet(X3,X4)))) = meet(X1,join(X2,meet(X3,meet(X4,join(X2,X1))))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.617.0.0']),
% 52.06/52.44 [weight('<11,156,9,[1,0,0,4]>')]).
% 52.06/52.44 cnf('0.617.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X3,meet(X4,join(X2,X1))))) = meet(X1,join(X2,meet(X1,meet(X3,X4)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.617.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_609]).
% 52.06/52.44 cnf('0.629.0.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X3,meet(join(X3,X1),X4)))) = meet(X1,meet(X2,meet(X1,join(X3,meet(X1,X4))))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.22.2.0','0.158.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.629.0.1',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X3,meet(join(X3,X1),X4)))) = meet(X1,meet(X2,join(X3,meet(X1,X4)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.629.0.0','0.22.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.629.1.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X3,meet(join(X3,X1),X4)))) = meet(X1,meet(X2,join(X3,meet(X1,X4)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.629.0.1']),
% 52.06/52.44 [weight('<11,158,22,[0,0,0,4]>')]).
% 52.06/52.44 cnf('0.629.2.0',plain,
% 52.06/52.44 ( meet(X1,meet(X2,join(X3,meet(join(X3,X1),X4)))) = meet(X1,meet(X2,join(X3,meet(X1,X4)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.629.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_621]).
% 52.06/52.44 cnf('0.697.0.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X1,join(X2,X4))))) = join(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.209.2.0','0.30.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.697.0.1',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X1,join(X2,X4))))) = join(X1,meet(X2,join(X3,X1))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.697.0.0','0.36.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.697.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X1,join(X2,X4))))) = join(X1,meet(X2,join(X3,X1))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.697.0.1']),
% 52.06/52.44 [weight('<11,209,30,[1,0,0,6]>')]).
% 52.06/52.44 cnf('0.697.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(X3,meet(X1,join(X2,X4))))) = join(X1,meet(X2,join(X3,X1))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.697.1.0',theory(equality)]),
% 52.06/52.44 [u,rule_689]).
% 52.06/52.44 cnf('0.816.0.0',plain,
% 52.06/52.44 ( join(X1,meet(meet(X2,X3),join(X4,X1))) = join(X1,meet(meet(X2,X3),join(X4,meet(X1,X3)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.697.2.0','0.143.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.816.0.1',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X3,join(X4,X1)))) = join(X1,meet(meet(X2,X3),join(X4,meet(X1,X3)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.816.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('0.816.0.2',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X3,join(X4,X1)))) = join(X1,meet(X2,meet(X3,join(X4,meet(X1,X3))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.816.0.1','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('R.2','L')]).
% 52.06/52.44 cnf('0.816.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X3,join(X4,X1)))) = join(X1,meet(X2,meet(X3,join(X4,meet(X1,X3))))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.816.0.2']),
% 52.06/52.44 [weight('<11,697,143,[1,0,0,6]>')]).
% 52.06/52.44 cnf('0.816.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X3,join(X4,meet(X1,X3))))) = join(X1,meet(X2,meet(X3,join(X4,X1)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.816.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_808]).
% 52.06/52.44 cnf('0.839.0.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X3,join(meet(X4,X3),X1)))) = join(X1,meet(X2,join(meet(X4,X3),meet(X1,X3)))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.816.2.0','0.121.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.839.1.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,meet(X3,join(meet(X4,X3),X1)))) = join(X1,meet(X2,join(meet(X4,X3),meet(X1,X3)))) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.839.0.0']),
% 52.06/52.44 [weight('<11,816,121,[1,0,0,4]>')]).
% 52.06/52.44 cnf('0.839.2.0',plain,
% 52.06/52.44 ( join(X1,meet(X2,join(meet(X3,X4),meet(X1,X4)))) = join(X1,meet(X2,meet(X4,join(meet(X3,X4),X1)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.839.1.0',theory(equality)]),
% 52.06/52.44 [x,rule_831]).
% 52.06/52.44 cnf('0.2471.0.0',plain,
% 52.06/52.44 ( meet(join(X1,meet(X2,meet(X3,X4))),X5) = meet(join(X1,meet(X2,meet(X3,X4))),meet(join(X1,X3),X5)) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.244.2.0','0.29.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.1.2','L')]).
% 52.06/52.44 cnf('0.2471.1.0',plain,
% 52.06/52.44 ( meet(join(X1,meet(X2,meet(X3,X4))),X5) = meet(join(X1,meet(X2,meet(X3,X4))),meet(join(X1,X3),X5)) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.2471.0.0']),
% 52.06/52.44 [weight('<13,244,29,[1,0,0,7]>')]).
% 52.06/52.44 cnf('0.2471.1.1',plain,
% 52.06/52.44 ( meet(join(X1,meet(X2,meet(X3,X4))),X5) = meet(join(X1,X3),meet(X5,join(X1,meet(X2,meet(X3,X4))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.2471.1.0','0.115.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','R')]).
% 52.06/52.44 cnf('0.2471.2.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(X4,meet(X2,X5))))) = meet(join(X1,meet(X4,meet(X2,X5))),X3) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.2471.1.1',theory(equality)]),
% 52.06/52.44 [x,rule_2463]).
% 52.06/52.44 cnf('0.3570.0.0',plain,
% 52.06/52.44 ( meet(meet(join(X1,X2),X3),join(X1,meet(meet(join(X1,X2),X3),meet(X2,X4)))) = meet(meet(join(X1,X2),X3),join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3)))))) ),
% 52.06/52.44 inference(cp,[status(thm)],['0.617.2.0','0.629.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','L')]).
% 52.06/52.44 cnf('0.3570.0.1',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(meet(join(X1,X2),X3),meet(X2,X4))))) = meet(meet(join(X1,X2),X3),join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3)))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.0.0','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.3570.0.2',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(join(X1,X2),meet(X3,meet(X2,X4)))))) = meet(meet(join(X1,X2),X3),join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3)))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.0.1','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.3570.0.3',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(X3,meet(X2,X4))))) = meet(meet(join(X1,X2),X3),join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3)))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.0.2','0.134.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('0.3570.0.4',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(X3,meet(X2,X4))))) = meet(join(X1,X2),meet(X3,join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3))))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.0.3','0.9.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.3570.0.5',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(X3,meet(X2,X4))))) = meet(join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3))))),X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.0.4','0.491.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.3570.1.0',plain,
% 52.06/52.44 ( meet(join(X1,X2),meet(X3,join(X1,meet(X3,meet(X2,X4))))) = meet(join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3))))),X3) ),
% 52.06/52.44 inference(weigh,[status(thm)],['0.3570.0.5']),
% 52.06/52.44 [weight('<13,629,617,[0,0,0,4]>')]).
% 52.06/52.44 cnf('0.3570.1.1',plain,
% 52.06/52.44 ( meet(join(X1,meet(X3,meet(X2,X4))),X3) = meet(join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3))))),X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.1.0','0.2471.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.3570.1.2',plain,
% 52.06/52.44 ( meet(X3,join(X1,meet(X3,meet(X2,X4)))) = meet(join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3))))),X3) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.1.1','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('0.3570.1.3',plain,
% 52.06/52.44 ( meet(X3,join(X1,meet(X3,meet(X2,X4)))) = meet(X3,join(X1,meet(X2,meet(X4,join(X1,meet(X2,X3)))))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['0.3570.1.2','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('R','L')]).
% 52.06/52.44 cnf('0.3570.2.0',plain,
% 52.06/52.44 ( meet(X1,join(X2,meet(X3,meet(X4,join(X2,meet(X3,X1)))))) = meet(X1,join(X2,meet(X1,meet(X3,X4)))) ),
% 52.06/52.44 inference(orient,[status(thm)],['0.3570.1.3',theory(equality)]),
% 52.06/52.44 [x,rule_3562]).
% 52.06/52.44 cnf('1.0.0.0',conjecture,
% 52.06/52.44 ( meet(a,join(b,meet(c,join(meet(a,d),meet(b,d))))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 file('/tmp/WALDMEISTER_495_n005',conjecture_1)).
% 52.06/52.44 cnf('1.0.0.1',plain,
% 52.06/52.44 ( meet(a,join(b,meet(c,meet(d,join(meet(a,d),b))))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.0','0.839.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2','L')]).
% 52.06/52.44 cnf('1.0.0.2',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(join(meet(a,d),b),c)))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.1','0.115.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','R')]).
% 52.06/52.44 cnf('1.0.0.3',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(c,join(meet(a,d),b))))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.2','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('1.0.0.4',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(c,join(b,meet(a,d)))))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.3','0.5.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2.2','L')]).
% 52.06/52.44 cnf('1.0.0.5',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(c,join(b,meet(d,a)))))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.4','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2.2.2','L')]).
% 52.06/52.44 cnf('1.0.0.6',plain,
% 52.06/52.44 ( meet(a,join(b,meet(a,meet(d,c)))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.5','0.3570.2.0',theory(equality)]),
% 52.06/52.44 [pos('L','L')]).
% 52.06/52.44 cnf('1.0.0.7',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(c,a)))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.6','0.115.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2','R')]).
% 52.06/52.44 cnf('1.0.0.8',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(a,c)))) = meet(a,join(b,meet(a,meet(c,d)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.7','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('L.2.2.2','L')]).
% 52.06/52.44 cnf('1.0.0.9',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(a,c)))) = meet(a,join(b,meet(d,meet(c,a)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.8','0.136.2.0',theory(equality)]),
% 52.06/52.44 [pos('R.2.2','L')]).
% 52.06/52.44 cnf('1.0.0.10',plain,
% 52.06/52.44 ( meet(a,join(b,meet(d,meet(a,c)))) = meet(a,join(b,meet(d,meet(a,c)))) ),
% 52.06/52.44 inference(reduction,[status(thm)],['1.0.0.9','0.8.2.0',theory(equality)]),
% 52.06/52.44 [pos('R.2.2.2','L')]).
% 52.06/52.44 cnf('1.0.0.11',plain,
% 52.06/52.44 ( $true ),
% 52.06/52.44 inference(trivial,[status(thm)],['1.0.0.10',theory(equality)]),
% 52.06/52.44 [conjecture_1]).
% 52.06/52.44
% 52.06/52.44 Proved Goals:
% 52.06/52.44 No. 1: meet(a,join(b,meet(c,join(meet(a,d),meet(b,d))))) ?= meet(a,join(b,meet(a,meet(c,d)))) joined, current: meet(a,join(b,meet(d,meet(a,c)))) = meet(a,join(b,meet(d,meet(a,c))))
% 52.06/52.44 1 goal was specified, which was proved.
% 52.06/52.44 % SZS output end CNFRefutation
% 52.06/52.44 #END OF PROOF
% 52.06/52.44
% 52.06/52.44 Problem WALDMEISTER_495_n005
% 52.06/52.44 CPs.gen 13046485
% 52.06/52.44 CPs.reexp 0
% 52.06/52.44 Select 234254
% 52.06/52.44 R 3562
% 52.06/52.44 E 8
% 52.06/52.44 vsize 11.2M
% 52.06/52.44 rss 6.7M
% 52.06/52.44 process.time 51.453s
% 52.06/52.44 wallclock.time 51.457s
% 52.06/52.44 status S
% 52.06/52.44
% 52.06/52.44
% 52.06/52.44 Waldmeister states: Goal proved.
% 52.06/52.44 % SZS status Unsatisfiable
%------------------------------------------------------------------------------