TSTP Solution File: LAT023-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT023-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 07:14:47 EDT 2022
% Result : Unsatisfiable 0.87s 1.27s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LAT023-1 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 30 03:35:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.97 * |/ | \/ | *
% 0.57/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.97 * A. Jaeger and B. Loechner | | *
% 0.57/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.57/0.97
% 0.57/0.97 Goals:
% 0.57/0.97 ------
% 0.57/0.97
% 0.57/0.97 ( 1) join(meet(a,b),meet(a,c)) ?=? meet(a,join(b,meet(a,c)))
% 0.57/0.97
% 0.57/0.97 Detected structure: Verband
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.87/1.27 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)))
% 0.87/1.27 goal joined
% 0.87/1.27 % SZS status Unsatisfiable
% 0.87/1.27 #START OF PROOF
% 0.87/1.27 % SZS output start CNFRefutation
% 0.87/1.27 cnf('0.1.0.0',axiom,
% 0.87/1.27 ( X1 = join(X1,X1) ),
% 0.87/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.87/1.27 cnf('0.1.1.0',plain,
% 0.87/1.27 ( X1 = join(X1,X1) ),
% 0.87/1.27 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.87/1.27 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.87/1.27 cnf('0.1.2.0',plain,
% 0.87/1.27 ( join(X1,X1) = X1 ),
% 0.87/1.27 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.87/1.27 [x,rule_1]).
% 0.87/1.27 cnf('0.2.0.0',axiom,
% 0.87/1.27 ( X1 = meet(X1,X1) ),
% 0.87/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.87/1.27 cnf('0.2.1.0',plain,
% 0.87/1.27 ( X1 = meet(X1,X1) ),
% 0.87/1.27 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.87/1.27 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.87/1.27 cnf('0.2.2.0',plain,
% 0.87/1.27 ( meet(X1,X1) = X1 ),
% 0.87/1.27 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.87/1.27 [x,rule_2]).
% 0.87/1.27 cnf('0.3.0.0',axiom,
% 0.87/1.27 ( join(X1,X2) = join(X2,X1) ),
% 0.87/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.87/1.27 cnf('0.3.1.0',plain,
% 0.91/1.27 ( join(X1,X2) = join(X2,X1) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.91/1.27 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.91/1.27 cnf('0.3.2.0',plain,
% 0.91/1.27 ( join(X1,X2) = join(X2,X1) ),
% 0.91/1.27 inference(activate,[status(thm)],['0.3.1.0']),
% 0.91/1.27 [equation_1]).
% 0.91/1.27 cnf('0.4.0.0',axiom,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.91/1.27 cnf('0.4.1.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.91/1.27 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.91/1.27 cnf('0.4.2.0',plain,
% 0.91/1.27 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_3]).
% 0.91/1.27 cnf('0.5.0.0',axiom,
% 0.91/1.27 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.91/1.27 cnf('0.5.1.0',plain,
% 0.91/1.27 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.91/1.27 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.91/1.27 cnf('0.5.2.0',plain,
% 0.91/1.27 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_4]).
% 0.91/1.27 cnf('0.6.0.0',axiom,
% 0.91/1.27 ( join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.91/1.27 cnf('0.6.1.0',plain,
% 0.91/1.27 ( join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.91/1.27 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.91/1.27 cnf('0.6.1.1',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.6.1.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.6.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.6.1.1',theory(equality)]),
% 0.91/1.27 [u,rule_5]).
% 0.91/1.27 cnf('0.7.0.0',axiom,
% 0.91/1.27 ( join(meet(join(X1,X2),X3),X2) = join(meet(join(X3,X2),X1),X2) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.91/1.27 cnf('0.7.1.0',plain,
% 0.91/1.27 ( join(meet(join(X1,X2),X3),X2) = join(meet(join(X3,X2),X1),X2) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.91/1.27 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.91/1.27 cnf('0.7.1.1',plain,
% 0.91/1.27 ( join(X2,meet(join(X1,X2),X3)) = join(meet(join(X3,X2),X1),X2) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.7.1.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.7.1.2',plain,
% 0.91/1.27 ( join(X2,meet(join(X1,X2),X3)) = join(X2,meet(join(X3,X2),X1)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.7.1.1','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.7.2.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(join(X3,X1),X2)) ),
% 0.91/1.27 inference(activate,[status(thm)],['0.7.1.2']),
% 0.91/1.27 [equation_2]).
% 0.91/1.27 cnf('0.8.0.0',axiom,
% 0.91/1.27 ( meet(X1,X2) = meet(X2,X1) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.91/1.27 cnf('0.8.1.0',plain,
% 0.91/1.27 ( meet(X1,X2) = meet(X2,X1) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.91/1.27 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.91/1.27 cnf('0.8.2.0',plain,
% 0.91/1.27 ( meet(X1,X2) = meet(X2,X1) ),
% 0.91/1.27 inference(activate,[status(thm)],['0.8.1.0']),
% 0.91/1.27 [equation_3]).
% 0.91/1.27 cnf('0.9.0.0',axiom,
% 0.91/1.27 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007')).
% 0.91/1.27 cnf('0.9.1.0',plain,
% 0.91/1.27 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.91/1.27 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.91/1.27 cnf('0.9.2.0',plain,
% 0.91/1.27 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_6]).
% 0.91/1.27 cnf('0.10.0.0',plain,
% 0.91/1.27 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.4.2.0','0.1.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.10.1.0',plain,
% 0.91/1.27 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.91/1.27 [weight('<5,4,1,[1,0,0,1]>')]).
% 0.91/1.27 cnf('0.10.2.0',plain,
% 0.91/1.27 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_7]).
% 0.91/1.27 cnf('0.11.0.0',plain,
% 0.91/1.27 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.9.2.0','0.2.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.11.1.0',plain,
% 0.91/1.27 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.91/1.27 [weight('<5,9,2,[1,0,0,1]>')]).
% 0.91/1.27 cnf('0.11.2.0',plain,
% 0.91/1.27 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_8]).
% 0.91/1.27 cnf('0.12.0.0',plain,
% 0.91/1.27 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.10.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.12.1.0',plain,
% 0.91/1.27 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.91/1.27 [weight('<5,10,3,[1,0,0,2]>')]).
% 0.91/1.27 cnf('0.12.2.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_9]).
% 0.91/1.27 cnf('0.13.0.0',plain,
% 0.91/1.27 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.11.2.0','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.13.1.0',plain,
% 0.91/1.27 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.91/1.27 [weight('<5,11,8,[1,0,0,2]>')]).
% 0.91/1.27 cnf('0.13.2.0',plain,
% 0.91/1.27 ( meet(X1,meet(X2,X1)) = meet(X1,X2) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_10]).
% 0.91/1.27 cnf('0.14.0.0',plain,
% 0.91/1.27 ( meet(X1,join(X1,X2)) = join(X1,meet(X1,join(X1,X2))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.14.1.0',plain,
% 0.91/1.27 ( meet(X1,join(X1,X2)) = join(X1,meet(X1,join(X1,X2))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.91/1.27 [weight('<7,6,2,[1,0,0,1]>')]).
% 0.91/1.27 cnf('0.14.2.0',plain,
% 0.91/1.27 ( join(X1,meet(X1,join(X1,X2))) = meet(X1,join(X1,X2)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_11]).
% 0.91/1.27 cnf('0.15.0.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X1)) = join(X1,meet(X1,X2)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.7.2.0','0.1.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1','L')]).
% 0.91/1.27 cnf('0.15.1.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X1)) = join(X1,meet(X1,X2)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.91/1.27 [weight('<7,7,1,[1,0,0,3]>')]).
% 0.91/1.27 cnf('0.15.1.1',plain,
% 0.91/1.27 ( join(X1,meet(X1,join(X2,X1))) = join(X1,meet(X1,X2)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.15.1.0','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.15.2.0',plain,
% 0.91/1.27 ( join(X1,meet(X1,join(X2,X1))) = join(X1,meet(X1,X2)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.15.1.1',theory(equality)]),
% 0.91/1.27 [u,rule_12]).
% 0.91/1.27 cnf('0.16.0.0',plain,
% 0.91/1.27 ( join(X1,meet(X1,X2)) = join(X1,meet(X1,join(X1,X2))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.15.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.2','L')]).
% 0.91/1.27 cnf('0.16.0.1',plain,
% 0.91/1.27 ( join(X1,meet(X1,X2)) = meet(X1,join(X1,X2)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.16.0.0','0.14.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.16.1.0',plain,
% 0.91/1.27 ( join(X1,meet(X1,X2)) = meet(X1,join(X1,X2)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.16.0.1']),
% 0.91/1.27 [weight('<5,15,3,[1,0,0,4]>')]).
% 0.91/1.27 cnf('0.16.2.0',plain,
% 0.91/1.27 ( join(X1,meet(X1,X2)) = meet(X1,join(X1,X2)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_13]).
% 0.91/1.27 cnf('0.18.0.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.7.2.0','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.18.1.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.91/1.27 [weight('<7,8,7,[0,0,0,2]>')]).
% 0.91/1.27 cnf('0.18.2.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_15]).
% 0.91/1.27 cnf('0.19.0.0',plain,
% 0.91/1.27 ( join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.4.2.0','0.12.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.19.0.1',plain,
% 0.91/1.27 ( join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.19.0.0','0.4.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.19.0.2',plain,
% 0.91/1.27 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.19.0.1','0.4.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.19.1.0',plain,
% 0.91/1.27 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.19.0.2']),
% 0.91/1.27 [weight('<7,12,4,[0,0,0,1]>')]).
% 0.91/1.27 cnf('0.19.2.0',plain,
% 0.91/1.27 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_16]).
% 0.91/1.27 cnf('0.20.0.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X1,join(X2,join(X3,X1))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.12.2.0','0.4.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.20.1.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X1,join(X2,join(X3,X1))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.91/1.27 [weight('<7,12,4,[1,0,0,2]>')]).
% 0.91/1.27 cnf('0.20.2.0',plain,
% 0.91/1.27 ( join(X1,join(X2,join(X3,X1))) = join(X1,join(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_17]).
% 0.91/1.27 cnf('0.21.0.0',plain,
% 0.91/1.27 ( meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.9.2.0','0.13.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.21.0.1',plain,
% 0.91/1.27 ( meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.21.0.0','0.9.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.21.0.2',plain,
% 0.91/1.27 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.21.0.1','0.9.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.21.1.0',plain,
% 0.91/1.27 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.21.0.2']),
% 0.91/1.27 [weight('<7,13,9,[0,0,0,1]>')]).
% 0.91/1.27 cnf('0.21.2.0',plain,
% 0.91/1.27 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_18]).
% 0.91/1.27 cnf('0.23.0.0',plain,
% 0.91/1.27 ( join(X1,join(meet(X1,X2),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.4.2.0','0.16.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.23.1.0',plain,
% 0.91/1.27 ( join(X1,join(meet(X1,X2),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.91/1.27 [weight('<7,16,4,[0,0,0,1]>')]).
% 0.91/1.27 cnf('0.23.2.0',plain,
% 0.91/1.27 ( join(meet(X1,join(X1,X2)),X3) = join(X1,join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_20]).
% 0.91/1.27 cnf('0.26.0.0',plain,
% 0.91/1.27 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(join(X1,X2),X3)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.18.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1','L')]).
% 0.91/1.27 cnf('0.26.1.0',plain,
% 0.91/1.27 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(join(X1,X2),X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.91/1.27 [weight('<7,18,3,[1,0,0,3]>')]).
% 0.91/1.27 cnf('0.26.2.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_23]).
% 0.91/1.27 cnf('0.30.0.0',plain,
% 0.91/1.27 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.91/1.27 cnf('0.30.1.0',plain,
% 0.91/1.27 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.91/1.27 [weight('<9,5,8,[0,0,0,0]>')]).
% 0.91/1.27 cnf('0.30.1.1',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.30.1.0','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.30.2.0',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.30.1.1',theory(equality)]),
% 0.91/1.27 [u,rule_27]).
% 0.91/1.27 cnf('0.31.0.0',plain,
% 0.91/1.27 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.6.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.2','L')]).
% 0.91/1.27 cnf('0.31.1.0',plain,
% 0.91/1.27 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.91/1.27 [weight('<9,6,3,[1,0,0,6]>')]).
% 0.91/1.27 cnf('0.31.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X2,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_28]).
% 0.91/1.27 cnf('0.53.0.0',plain,
% 0.91/1.27 ( join(X1,join(meet(join(X1,X2),X3),X4)) = join(join(X1,meet(X2,join(X3,X1))),X4) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.4.2.0','0.26.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.53.0.1',plain,
% 0.91/1.27 ( join(X1,join(meet(join(X1,X2),X3),X4)) = join(X1,join(meet(X2,join(X3,X1)),X4)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.53.0.0','0.4.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.53.1.0',plain,
% 0.91/1.27 ( join(X1,join(meet(join(X1,X2),X3),X4)) = join(X1,join(meet(X2,join(X3,X1)),X4)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.53.0.1']),
% 0.91/1.27 [weight('<9,26,4,[0,0,0,1]>')]).
% 0.91/1.27 cnf('0.53.2.0',plain,
% 0.91/1.27 ( join(X1,join(meet(join(X1,X2),X3),X4)) = join(X1,join(meet(X2,join(X3,X1)),X4)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_49]).
% 0.91/1.27 cnf('0.54.0.0',plain,
% 0.91/1.27 ( join(X1,join(X2,meet(join(X1,X3),X4))) = join(X1,join(X2,join(X1,meet(X3,join(X4,X1))))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.19.2.0','0.26.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.2','L')]).
% 0.91/1.27 cnf('0.54.0.1',plain,
% 0.91/1.27 ( join(X1,join(X2,meet(join(X1,X3),X4))) = join(X1,join(X2,meet(X3,join(X4,X1)))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.54.0.0','0.19.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.54.1.0',plain,
% 0.91/1.27 ( join(X1,join(X2,meet(join(X1,X3),X4))) = join(X1,join(X2,meet(X3,join(X4,X1)))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.54.0.1']),
% 0.91/1.27 [weight('<9,26,19,[0,0,0,4]>')]).
% 0.91/1.27 cnf('0.54.2.0',plain,
% 0.91/1.27 ( join(X1,join(X2,meet(join(X1,X3),X4))) = join(X1,join(X2,meet(X3,join(X4,X1)))) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_50]).
% 0.91/1.27 cnf('0.63.0.0',plain,
% 0.91/1.27 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X3,X2))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.31.2.0','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.63.1.0',plain,
% 0.91/1.27 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X3,X2))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.63.0.0']),
% 0.91/1.27 [weight('<9,31,8,[1,0,0,1]>')]).
% 0.91/1.27 cnf('0.63.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X1,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_59]).
% 0.91/1.27 cnf('0.64.0.0',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,join(meet(X1,X2),meet(join(X1,X2),join(X3,X1)))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.63.2.0','0.23.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.64.0.1',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,join(meet(X1,X2),meet(X2,join(join(X3,X1),X1)))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.64.0.0','0.54.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.64.0.2',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X1,join(X3,X1)))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.64.0.1','0.63.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.2','L')]).
% 0.91/1.27 cnf('0.64.0.3',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X1,X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.64.0.2','0.12.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.2.2','L')]).
% 0.91/1.27 cnf('0.64.1.0',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X1,X3))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.64.0.3']),
% 0.91/1.27 [weight('<7,63,23,[1,0,0,0]>')]).
% 0.91/1.27 cnf('0.64.2.0',plain,
% 0.91/1.27 ( join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X2),join(X1,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_60]).
% 0.91/1.27 cnf('0.65.0.0',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.64.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.2','L')]).
% 0.91/1.27 cnf('0.65.1.0',plain,
% 0.91/1.27 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.65.0.0']),
% 0.91/1.27 [weight('<7,64,3,[1,0,0,4]>')]).
% 0.91/1.27 cnf('0.65.2.0',plain,
% 0.91/1.27 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X1,X2),join(X1,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_61]).
% 0.91/1.27 cnf('0.66.0.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 0.91/1.27 inference(interreduction_right,[status(thm)],['0.18.2.0'])).
% 0.91/1.27 cnf('0.66.0.1',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.66.0.0','0.65.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.66.1.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.66.0.1']),
% 0.91/1.27 [weight('<7,18,65,[0,0,0,0]>')]).
% 0.91/1.27 cnf('0.66.2.0',plain,
% 0.91/1.27 ( join(X1,meet(join(X2,X1),X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_62]).
% 0.91/1.27 cnf('0.238.0.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.4.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.238.1.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.238.0.0']),
% 0.91/1.27 [weight('<10,4,3,[1,0,0,0]>')]).
% 0.91/1.27 cnf('0.238.2.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 0.91/1.27 inference(activate,[status(thm)],['0.238.1.0']),
% 0.91/1.27 [equation_19]).
% 0.91/1.27 cnf('0.244.0.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X3,join(X2,X1)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.238.2.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.2','L')]).
% 0.91/1.27 cnf('0.244.1.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X3,join(X2,X1)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.244.0.0']),
% 0.91/1.27 [weight('<10,238,3,[1,1,0,2]>')]).
% 0.91/1.27 cnf('0.244.2.0',plain,
% 0.91/1.27 ( join(X1,join(X2,X3)) = join(X3,join(X2,X1)) ),
% 0.91/1.27 inference(activate,[status(thm)],['0.244.1.0']),
% 0.91/1.27 [equation_25]).
% 0.91/1.27 cnf('0.245.0.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,join(X2,X3)),X4)) = join(meet(X1,join(X2,X3)),X4) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.4.2.0','0.6.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.245.1.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,join(X2,X3)),X4)) = join(meet(X1,join(X2,X3)),X4) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.245.0.0']),
% 0.91/1.27 [weight('<11,6,4,[0,0,0,1]>')]).
% 0.91/1.27 cnf('0.245.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,join(X2,X3)),X4)) = join(meet(X1,join(X2,X3)),X4) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.245.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_220]).
% 0.91/1.27 cnf('0.246.0.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.246.1.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.246.0.0']),
% 0.91/1.27 [weight('<11,11,6,[0,0,0,1]>')]).
% 0.91/1.27 cnf('0.246.1.1',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(join(meet(X1,X2),X1),join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.246.1.0','0.64.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.246.1.2',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(join(X1,meet(X1,X2)),join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.246.1.1','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.1','L')]).
% 0.91/1.27 cnf('0.246.1.3',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(meet(X1,join(X1,X2)),join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.246.1.2','0.16.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.1','L')]).
% 0.91/1.27 cnf('0.246.1.4',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,meet(join(X1,X2),join(meet(X1,X2),X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.246.1.3','0.9.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.246.2.0',plain,
% 0.91/1.27 ( meet(X1,meet(join(X1,X2),join(meet(X1,X2),X3))) = meet(X1,join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.246.1.4',theory(equality)]),
% 0.91/1.27 [x,rule_221]).
% 0.91/1.27 cnf('0.248.0.0',plain,
% 0.91/1.27 ( join(meet(X1,join(X2,X3)),join(X4,meet(X1,X2))) = join(meet(X1,join(X2,X3)),join(X4,meet(X1,join(X2,X3)))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.20.2.0','0.6.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.2','L')]).
% 0.91/1.27 cnf('0.248.0.1',plain,
% 0.91/1.27 ( join(meet(X1,join(X2,X3)),join(X4,meet(X1,X2))) = join(meet(X1,join(X2,X3)),X4) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.248.0.0','0.12.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.248.1.0',plain,
% 0.91/1.27 ( join(meet(X1,join(X2,X3)),join(X4,meet(X1,X2))) = join(meet(X1,join(X2,X3)),X4) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.248.0.1']),
% 0.91/1.27 [weight('<11,20,6,[1,0,0,4]>')]).
% 0.91/1.27 cnf('0.248.1.1',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(X4,meet(X1,join(X2,X3)))) = join(meet(X1,join(X2,X3)),X4) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.248.1.0','0.244.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.248.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(X3,meet(X1,join(X2,X4)))) = join(meet(X1,join(X2,X4)),X3) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.248.1.1',theory(equality)]),
% 0.91/1.27 [u,rule_223]).
% 0.91/1.27 cnf('0.290.0.0',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(join(X1,meet(X2,X3)),X1)),X4)) = join(X1,join(join(X1,meet(X2,X3)),X4)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.53.2.0','0.30.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1','L')]).
% 0.91/1.27 cnf('0.290.0.1',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(X1,join(meet(X2,X3),X1))),X4)) = join(X1,join(join(X1,meet(X2,X3)),X4)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.290.0.0','0.4.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1.2','L')]).
% 0.91/1.27 cnf('0.290.0.2',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(X1,meet(X2,X3))),X4)) = join(X1,join(join(X1,meet(X2,X3)),X4)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.290.0.1','0.12.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1.2','L')]).
% 0.91/1.27 cnf('0.290.0.3',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(X1,meet(X2,X3))),X4)) = join(X1,join(X1,join(meet(X2,X3),X4))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.290.0.2','0.4.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.2','L')]).
% 0.91/1.27 cnf('0.290.0.4',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(X1,meet(X2,X3))),X4)) = join(X1,join(meet(X2,X3),X4)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.290.0.3','0.10.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.290.1.0',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(X1,meet(X2,X3))),X4)) = join(X1,join(meet(X2,X3),X4)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.290.0.4']),
% 0.91/1.27 [weight('<11,53,30,[1,0,0,3]>')]).
% 0.91/1.27 cnf('0.290.2.0',plain,
% 0.91/1.27 ( join(X1,join(meet(X2,join(X1,meet(X2,X3))),X4)) = join(X1,join(meet(X2,X3),X4)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.290.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_262]).
% 0.91/1.27 cnf('0.314.0.0',plain,
% 0.91/1.27 ( meet(join(meet(X1,X2),X1),join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(meet(X1,join(X1,X2)),X3)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.66.2.0','0.16.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1','L')]).
% 0.91/1.27 cnf('0.314.0.1',plain,
% 0.91/1.27 ( meet(join(meet(X1,X2),X1),join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.314.0.0','0.9.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.2','L')]).
% 0.91/1.27 cnf('0.314.1.0',plain,
% 0.91/1.27 ( meet(join(meet(X1,X2),X1),join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.314.0.1']),
% 0.91/1.27 [weight('<11,66,16,[1,0,0,3]>')]).
% 0.91/1.27 cnf('0.314.1.1',plain,
% 0.91/1.27 ( meet(join(X1,meet(X1,X2)),join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.314.1.0','0.3.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.314.1.2',plain,
% 0.91/1.27 ( meet(meet(X1,join(X1,X2)),join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.314.1.1','0.16.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.1','L')]).
% 0.91/1.27 cnf('0.314.1.3',plain,
% 0.91/1.27 ( meet(X1,meet(join(X1,X2),join(meet(X1,X2),X3))) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.314.1.2','0.9.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.314.1.4',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.314.1.3','0.246.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.314.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) = meet(X1,join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.314.1.4',theory(equality)]),
% 0.91/1.27 [x,rule_285]).
% 0.91/1.27 cnf('0.315.0.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,meet(join(X1,X2),X3))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.314.2.0','0.21.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.315.0.1',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = meet(X1,join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.315.0.0','0.314.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.315.1.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = meet(X1,join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.315.0.1']),
% 0.91/1.27 [weight('<9,314,21,[1,0,0,4]>')]).
% 0.91/1.27 cnf('0.315.2.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = meet(X1,join(meet(X1,X2),X3)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.315.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_286]).
% 0.91/1.27 cnf('0.316.0.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,meet(X1,X2)),meet(X1,join(meet(X1,X3),X2))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.31.2.0','0.315.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.316.0.1',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,meet(X1,X2)),meet(X1,join(meet(X1,X3),X2))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.316.0.0','0.315.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.316.0.2',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,join(meet(X1,X3),X2))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.316.0.1','0.11.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.1','L')]).
% 0.91/1.27 cnf('0.316.0.3',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.316.0.2','0.31.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.316.1.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.316.0.3']),
% 0.91/1.27 [weight('<7,315,31,[0,0,0,4]>')]).
% 0.91/1.27 cnf('0.316.2.0',plain,
% 0.91/1.27 ( meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.316.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_287]).
% 0.91/1.27 cnf('0.323.0.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,X3),X4)) = join(meet(X1,X2),join(meet(X1,join(X2,meet(X1,meet(X1,X3)))),X4)) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.290.2.0','0.316.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.1','L')]).
% 0.91/1.27 cnf('0.323.0.1',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,X3),X4)) = join(meet(X1,join(X2,meet(X1,meet(X1,X3)))),X4) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.323.0.0','0.245.2.0',theory(equality)]),
% 0.91/1.27 [pos('R','L')]).
% 0.91/1.27 cnf('0.323.0.2',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,X3),X4)) = join(meet(X1,join(X2,meet(X1,X3))),X4) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.323.0.1','0.11.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.1.2.2','L')]).
% 0.91/1.27 cnf('0.323.1.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,X3),X4)) = join(meet(X1,join(X2,meet(X1,X3))),X4) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.323.0.2']),
% 0.91/1.27 [weight('<9,316,290,[0,0,0,3]>')]).
% 0.91/1.27 cnf('0.323.2.0',plain,
% 0.91/1.27 ( join(meet(X1,join(X2,meet(X1,X3))),X4) = join(meet(X1,X2),join(meet(X1,X3),X4)) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.323.1.0',theory(equality)]),
% 0.91/1.27 [x,rule_294]).
% 0.91/1.27 cnf('0.324.0.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,X3),meet(X1,join(X2,meet(X1,X3))))) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(cp,[status(thm)],['0.323.2.0','0.1.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.324.0.1',plain,
% 0.91/1.27 ( join(meet(X1,join(X2,meet(X1,X3))),meet(X1,X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.324.0.0','0.248.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.324.0.2',plain,
% 0.91/1.27 ( join(meet(X1,X2),join(meet(X1,X3),meet(X1,X3))) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.324.0.1','0.323.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('0.324.0.3',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['0.324.0.2','0.1.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2','L')]).
% 0.91/1.27 cnf('0.324.1.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(weigh,[status(thm)],['0.324.0.3']),
% 0.91/1.27 [weight('<7,323,1,[1,0,0,0]>')]).
% 0.91/1.27 cnf('0.324.2.0',plain,
% 0.91/1.27 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,meet(X1,X3))) ),
% 0.91/1.27 inference(orient,[status(thm)],['0.324.1.0',theory(equality)]),
% 0.91/1.27 [u,rule_295]).
% 0.91/1.27 cnf('1.0.0.0',conjecture,
% 0.91/1.27 ( join(meet(a,b),meet(a,c)) = meet(a,join(b,meet(a,c))) ),
% 0.91/1.27 file('/tmp/WALDMEISTER_7609_n007',conjecture_1)).
% 0.91/1.27 cnf('1.0.0.1',plain,
% 0.91/1.27 ( meet(a,join(b,meet(a,c))) = meet(a,join(b,meet(a,c))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['1.0.0.0','0.324.2.0',theory(equality)]),
% 0.91/1.27 [pos('L','L')]).
% 0.91/1.27 cnf('1.0.0.2',plain,
% 0.91/1.27 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(a,c))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['1.0.0.1','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('L.2.2','L')]).
% 0.91/1.27 cnf('1.0.0.3',plain,
% 0.91/1.27 ( meet(a,join(b,meet(c,a))) = meet(a,join(b,meet(c,a))) ),
% 0.91/1.27 inference(reduction,[status(thm)],['1.0.0.2','0.8.2.0',theory(equality)]),
% 0.91/1.27 [pos('R.2.2','L')]).
% 0.91/1.27 cnf('1.0.0.4',plain,
% 0.91/1.27 ( $true ),
% 0.91/1.27 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 0.91/1.27 [conjecture_1]).
% 0.91/1.27
% 0.91/1.27 Proved Goals:
% 0.91/1.27 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)))
% 0.91/1.27 1 goal was specified, which was proved.
% 0.91/1.27 % SZS output end CNFRefutation
% 0.91/1.27 #END OF PROOF
% 0.91/1.27
% 0.91/1.27 Problem WALDMEISTER_7609_n007
% 0.91/1.27 CPs.gen 83540
% 0.91/1.27 CPs.reexp 0
% 0.91/1.27 Select 2071
% 0.91/1.27 R 295
% 0.91/1.27 E 29
% 0.91/1.27 vsize 6.5M
% 0.91/1.27 rss 3.8M
% 0.91/1.27 process.time 0.308s
% 0.91/1.27 wallclock.time 0.308s
% 0.91/1.27 status S
% 0.91/1.27
% 0.91/1.27
% 0.91/1.27 Waldmeister states: Goal proved.
% 0.91/1.27 % SZS status Unsatisfiable
%------------------------------------------------------------------------------