TSTP Solution File: LAT010-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n011.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 07:14:40 EDT 2022
% Result : Unsatisfiable 3.57s 3.98s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n011.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 01:13:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/1.00 ********************************************************************************
% 0.59/1.00 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/1.00 * |/ | \/ | *
% 0.59/1.00 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/1.00 * A. Jaeger and B. Loechner | | *
% 0.59/1.00 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/1.00 ********************************************************************************
% 0.59/1.00
% 0.59/1.00
% 0.59/1.00 Goals:
% 0.59/1.00 ------
% 0.59/1.00
% 0.59/1.00 ( 1) meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))) ?=? meet(a,meet(join(b,c),join(b,d)))
% 0.59/1.00
% 0.59/1.00 Detected structure: Verband
% 0.59/1.00 ********************************************************************************
% 0.59/1.00 ****************************** COMPLETION - PROOF ******************************
% 0.59/1.00 ********************************************************************************
% 0.59/1.00
% 3.57/3.98 joined goal: 1 meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))) ?= meet(a,meet(join(b,c),join(b,d))) to meet(a,meet(join(d,b),join(c,b)))
% 3.57/3.98 goal joined
% 3.57/3.98 % SZS status Unsatisfiable
% 3.57/3.98 #START OF PROOF
% 3.57/3.98 % SZS output start CNFRefutation
% 3.57/3.98 cnf('0.1.0.0',axiom,
% 3.57/3.98 ( X1 = meet(X1,X1) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.1.1.0',plain,
% 3.57/3.98 ( X1 = meet(X1,X1) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.1.0.0']),
% 3.57/3.98 [weight('<0,0,0,[0,0,0,1]>')]).
% 3.57/3.98 cnf('0.1.2.0',plain,
% 3.57/3.98 ( meet(X1,X1) = X1 ),
% 3.57/3.98 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_1]).
% 3.57/3.98 cnf('0.2.0.0',axiom,
% 3.57/3.98 ( X1 = meet(X1,join(X1,X2)) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.2.1.0',plain,
% 3.57/3.98 ( X1 = meet(X1,join(X1,X2)) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.2.0.0']),
% 3.57/3.98 [weight('<1,0,0,[0,0,0,2]>')]).
% 3.57/3.98 cnf('0.2.2.0',plain,
% 3.57/3.98 ( meet(X1,join(X1,X2)) = X1 ),
% 3.57/3.98 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_2]).
% 3.57/3.98 cnf('0.3.0.0',axiom,
% 3.57/3.98 ( X1 = join(X1,X1) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.3.1.0',plain,
% 3.57/3.98 ( X1 = join(X1,X1) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.3.0.0']),
% 3.57/3.98 [weight('<2,0,0,[0,0,0,3]>')]).
% 3.57/3.98 cnf('0.3.2.0',plain,
% 3.57/3.98 ( join(X1,X1) = X1 ),
% 3.57/3.98 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_3]).
% 3.57/3.98 cnf('0.4.0.0',axiom,
% 3.57/3.98 ( X1 = join(X1,meet(X1,X2)) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.4.1.0',plain,
% 3.57/3.98 ( X1 = join(X1,meet(X1,X2)) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.4.0.0']),
% 3.57/3.98 [weight('<3,0,0,[0,0,0,4]>')]).
% 3.57/3.98 cnf('0.4.2.0',plain,
% 3.57/3.98 ( join(X1,meet(X1,X2)) = X1 ),
% 3.57/3.98 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_4]).
% 3.57/3.98 cnf('0.5.0.0',axiom,
% 3.57/3.98 ( meet(X1,X2) = meet(X2,X1) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.5.1.0',plain,
% 3.57/3.98 ( meet(X1,X2) = meet(X2,X1) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.5.0.0']),
% 3.57/3.98 [weight('<4,0,0,[0,0,0,5]>')]).
% 3.57/3.98 cnf('0.5.2.0',plain,
% 3.57/3.98 ( meet(X1,X2) = meet(X2,X1) ),
% 3.57/3.98 inference(activate,[status(thm)],['0.5.1.0']),
% 3.57/3.98 [equation_1]).
% 3.57/3.98 cnf('0.6.0.0',axiom,
% 3.57/3.98 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.6.1.0',plain,
% 3.57/3.98 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.6.0.0']),
% 3.57/3.98 [weight('<5,0,0,[0,0,0,6]>')]).
% 3.57/3.98 cnf('0.6.2.0',plain,
% 3.57/3.98 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 3.57/3.98 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_5]).
% 3.57/3.98 cnf('0.8.0.0',axiom,
% 3.57/3.98 ( meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))) = join(meet(X3,join(X1,meet(X2,X3))),meet(X1,join(X2,X3))) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.8.1.0',plain,
% 3.57/3.98 ( meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))) = join(meet(X3,join(X1,meet(X2,X3))),meet(X1,join(X2,X3))) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.8.0.0']),
% 3.57/3.98 [weight('<7,0,0,[0,0,0,8]>')]).
% 3.57/3.98 cnf('0.8.2.0',plain,
% 3.57/3.98 ( join(meet(X1,join(X2,meet(X3,X1))),meet(X2,join(X3,X1))) = meet(join(X2,meet(X3,X1)),join(X1,meet(X2,X3))) ),
% 3.57/3.98 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_7]).
% 3.57/3.98 cnf('0.10.0.0',axiom,
% 3.57/3.98 ( join(X1,X2) = join(X2,X1) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.10.1.0',plain,
% 3.57/3.98 ( join(X1,X2) = join(X2,X1) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.10.0.0']),
% 3.57/3.98 [weight('<9,0,0,[0,0,0,10]>')]).
% 3.57/3.98 cnf('0.10.2.0',plain,
% 3.57/3.98 ( join(X1,X2) = join(X2,X1) ),
% 3.57/3.98 inference(activate,[status(thm)],['0.10.1.0']),
% 3.57/3.98 [equation_2]).
% 3.57/3.98 cnf('0.11.0.0',axiom,
% 3.57/3.98 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 3.57/3.98 file('/tmp/WALDMEISTER_26737_n011')).
% 3.57/3.98 cnf('0.11.1.0',plain,
% 3.57/3.98 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.11.0.0']),
% 3.57/3.98 [weight('<10,0,0,[0,0,0,11]>')]).
% 3.57/3.98 cnf('0.11.2.0',plain,
% 3.57/3.98 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 3.57/3.98 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_9]).
% 3.57/3.98 cnf('0.12.0.0',plain,
% 3.57/3.98 ( X1 = join(X1,meet(X2,X1)) ),
% 3.57/3.98 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 3.57/3.98 [pos('L.2','L')]).
% 3.57/3.98 cnf('0.12.1.0',plain,
% 3.57/3.98 ( X1 = join(X1,meet(X2,X1)) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.12.0.0']),
% 3.57/3.98 [weight('<5,5,4,[0,0,0,2]>')]).
% 3.57/3.98 cnf('0.12.2.0',plain,
% 3.57/3.98 ( join(X1,meet(X2,X1)) = X1 ),
% 3.57/3.98 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_10]).
% 3.57/3.98 cnf('0.13.0.0',plain,
% 3.57/3.98 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 3.57/3.98 inference(cp,[status(thm)],['0.6.2.0','0.1.2.0',theory(equality)]),
% 3.57/3.98 [pos('L.1','L')]).
% 3.57/3.98 cnf('0.13.1.0',plain,
% 3.57/3.98 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.13.0.0']),
% 3.57/3.98 [weight('<5,6,1,[1,0,0,1]>')]).
% 3.57/3.98 cnf('0.13.2.0',plain,
% 3.57/3.98 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 3.57/3.98 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 3.57/3.98 [u,rule_11]).
% 3.57/3.98 cnf('0.14.0.0',plain,
% 3.57/3.98 ( X1 = meet(X1,join(X2,X1)) ),
% 3.57/3.98 inference(cp,[status(thm)],['0.2.2.0','0.10.2.0',theory(equality)]),
% 3.57/3.98 [pos('L.2','L')]).
% 3.57/3.98 cnf('0.14.1.0',plain,
% 3.57/3.98 ( X1 = meet(X1,join(X2,X1)) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.14.0.0']),
% 3.57/3.98 [weight('<5,10,2,[0,0,0,2]>')]).
% 3.57/3.98 cnf('0.14.2.0',plain,
% 3.57/3.98 ( meet(X1,join(X2,X1)) = X1 ),
% 3.57/3.98 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_12]).
% 3.57/3.98 cnf('0.15.0.0',plain,
% 3.57/3.98 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 3.57/3.98 inference(cp,[status(thm)],['0.11.2.0','0.3.2.0',theory(equality)]),
% 3.57/3.98 [pos('L.1','L')]).
% 3.57/3.98 cnf('0.15.1.0',plain,
% 3.57/3.98 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.15.0.0']),
% 3.57/3.98 [weight('<5,11,3,[1,0,0,1]>')]).
% 3.57/3.98 cnf('0.15.2.0',plain,
% 3.57/3.98 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 3.57/3.98 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 3.57/3.98 [u,rule_13]).
% 3.57/3.98 cnf('0.17.0.0',plain,
% 3.57/3.98 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 3.57/3.98 inference(cp,[status(thm)],['0.13.2.0','0.5.2.0',theory(equality)]),
% 3.57/3.98 [pos('L.2','L')]).
% 3.57/3.98 cnf('0.17.1.0',plain,
% 3.57/3.98 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 3.57/3.98 inference(weigh,[status(thm)],['0.17.0.0']),
% 3.57/3.98 [weight('<5,13,5,[1,0,0,2]>')]).
% 3.57/3.98 cnf('0.17.2.0',plain,
% 3.57/3.98 ( meet(X1,meet(X2,X1)) = meet(X1,X2) ),
% 3.57/3.98 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 3.57/3.98 [x,rule_15]).
% 3.57/3.98 cnf('0.18.0.0',plain,
% 3.57/3.98 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 3.57/3.98 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.18.1.0',plain,
% 3.57/3.99 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.18.0.0']),
% 3.57/3.99 [weight('<7,6,2,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.18.2.0',plain,
% 3.57/3.99 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_16]).
% 3.57/3.99 cnf('0.19.0.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.11.2.0','0.4.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.19.1.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.19.0.0']),
% 3.57/3.99 [weight('<7,11,4,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.19.2.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_17]).
% 3.57/3.99 cnf('0.20.0.0',plain,
% 3.57/3.99 ( X1 = join(X1,meet(X2,meet(X3,X1))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.20.1.0',plain,
% 3.57/3.99 ( X1 = join(X1,meet(X2,meet(X3,X1))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.20.0.0']),
% 3.57/3.99 [weight('<7,12,6,[1,0,0,2]>')]).
% 3.57/3.99 cnf('0.20.2.0',plain,
% 3.57/3.99 ( join(X1,meet(X2,meet(X3,X1))) = X1 ),
% 3.57/3.99 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_18]).
% 3.57/3.99 cnf('0.21.0.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.11.2.0','0.12.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.21.1.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.21.0.0']),
% 3.57/3.99 [weight('<7,12,11,[0,0,0,1]>')]).
% 3.57/3.99 cnf('0.21.2.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_19]).
% 3.57/3.99 cnf('0.27.0.0',plain,
% 3.57/3.99 ( meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.6.2.0','0.17.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.27.0.1',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.27.0.0','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.27.0.2',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.27.0.1','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.27.1.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.27.0.2']),
% 3.57/3.99 [weight('<7,17,6,[0,0,0,1]>')]).
% 3.57/3.99 cnf('0.27.2.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_25]).
% 3.57/3.99 cnf('0.32.0.0',plain,
% 3.57/3.99 ( join(X1,X2) = join(X1,join(X2,meet(X1,X3))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.19.2.0','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.32.1.0',plain,
% 3.57/3.99 ( join(X1,X2) = join(X1,join(X2,meet(X1,X3))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.32.0.0']),
% 3.57/3.99 [weight('<7,19,10,[1,0,0,2]>')]).
% 3.57/3.99 cnf('0.32.2.0',plain,
% 3.57/3.99 ( join(X1,join(X2,meet(X1,X3))) = join(X1,X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_30]).
% 3.57/3.99 cnf('0.34.0.0',plain,
% 3.57/3.99 ( join(X1,X2) = join(join(X1,X2),meet(X3,X1)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.20.2.0','0.2.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2','L')]).
% 3.57/3.99 cnf('0.34.0.1',plain,
% 3.57/3.99 ( join(X1,X2) = join(X1,join(X2,meet(X3,X1))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.34.0.0','0.11.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.34.1.0',plain,
% 3.57/3.99 ( join(X1,X2) = join(X1,join(X2,meet(X3,X1))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.34.0.1']),
% 3.57/3.99 [weight('<7,20,2,[1,0,0,4]>')]).
% 3.57/3.99 cnf('0.34.2.0',plain,
% 3.57/3.99 ( join(X1,join(X2,meet(X3,X1))) = join(X1,X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_32]).
% 3.57/3.99 cnf('0.41.0.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.14.2.0','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.41.1.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.41.0.0']),
% 3.57/3.99 [weight('<9,14,6,[1,0,0,0]>')]).
% 3.57/3.99 cnf('0.41.2.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_39]).
% 3.57/3.99 cnf('0.42.0.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.12.2.0','0.18.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.42.1.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.42.0.0']),
% 3.57/3.99 [weight('<9,18,12,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.42.1.1',plain,
% 3.57/3.99 ( meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.42.1.0','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.42.2.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.42.1.1',theory(equality)]),
% 3.57/3.99 [x,rule_40]).
% 3.57/3.99 cnf('0.43.0.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),meet(X1,X3)) = join(meet(X1,X3),meet(join(X1,X2),meet(X1,X3))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.42.2.0','0.13.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.43.0.1',plain,
% 3.57/3.99 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.43.0.0','0.12.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.43.1.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.43.0.1']),
% 3.57/3.99 [weight('<7,42,13,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.43.2.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_41]).
% 3.57/3.99 cnf('0.45.0.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(join(X3,X1),meet(X1,X2)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.43.2.0','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.45.1.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(join(X3,X1),meet(X1,X2)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.45.0.0']),
% 3.57/3.99 [weight('<7,43,10,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.45.2.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),meet(X2,X3)) = meet(X2,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_43]).
% 3.57/3.99 cnf('0.47.0.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.14.2.0','0.19.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.47.1.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.47.0.0']),
% 3.57/3.99 [weight('<9,19,14,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.47.1.1',plain,
% 3.57/3.99 ( join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.47.1.0','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.47.2.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.47.1.1',theory(equality)]),
% 3.57/3.99 [x,rule_45]).
% 3.57/3.99 cnf('0.48.0.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),join(X1,X3)) = meet(join(X1,X3),join(meet(X1,X2),join(X1,X3))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.47.2.0','0.15.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.48.0.1',plain,
% 3.57/3.99 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.48.0.0','0.14.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.48.1.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.48.0.1']),
% 3.57/3.99 [weight('<7,47,15,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.48.2.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_46]).
% 3.57/3.99 cnf('0.50.0.0',plain,
% 3.57/3.99 ( join(X1,X2) = join(meet(X1,X3),join(X2,X1)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.48.2.0','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.50.1.0',plain,
% 3.57/3.99 ( join(X1,X2) = join(meet(X1,X3),join(X2,X1)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.50.0.0']),
% 3.57/3.99 [weight('<7,48,10,[1,0,0,4]>')]).
% 3.57/3.99 cnf('0.50.2.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),join(X3,X1)) = join(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_48]).
% 3.57/3.99 cnf('0.56.0.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.14.2.0','0.21.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.56.1.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X2,X3)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.56.0.0']),
% 3.57/3.99 [weight('<9,21,14,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.56.1.1',plain,
% 3.57/3.99 ( join(meet(X1,X2),X3) = meet(join(X2,X3),join(meet(X1,X2),X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.56.1.0','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.56.2.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),join(meet(X3,X1),X2)) = join(meet(X3,X1),X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.56.1.1',theory(equality)]),
% 3.57/3.99 [x,rule_54]).
% 3.57/3.99 cnf('0.76.0.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(join(X1,X3),X4))) = meet(X1,meet(join(X1,X3),meet(X2,X4))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.18.2.0','0.27.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.76.0.1',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(join(X1,X3),X4))) = meet(X1,meet(X2,X4)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.76.0.0','0.18.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.76.1.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(join(X1,X3),X4))) = meet(X1,meet(X2,X4)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.76.0.1']),
% 3.57/3.99 [weight('<9,27,18,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.76.2.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,meet(join(X1,X3),X4))) = meet(X1,meet(X2,X4)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 3.57/3.99 [u,rule_74]).
% 3.57/3.99 cnf('0.88.0.0',plain,
% 3.57/3.99 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X3,X1)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.14.2.0','0.34.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.88.1.0',plain,
% 3.57/3.99 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X3,X1)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.88.0.0']),
% 3.57/3.99 [weight('<9,34,14,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.88.1.1',plain,
% 3.57/3.99 ( join(X1,meet(X2,X3)) = meet(join(X3,X1),join(X1,meet(X2,X3))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.88.1.0','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.88.2.0',plain,
% 3.57/3.99 ( meet(join(X1,X2),join(X2,meet(X3,X1))) = join(X2,meet(X3,X1)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.88.1.1',theory(equality)]),
% 3.57/3.99 [x,rule_86]).
% 3.57/3.99 cnf('0.97.0.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.41.2.0','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2.2','L')]).
% 3.57/3.99 cnf('0.97.1.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.97.0.0']),
% 3.57/3.99 [weight('<9,41,5,[1,0,0,6]>')]).
% 3.57/3.99 cnf('0.97.2.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.97.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_95]).
% 3.57/3.99 cnf('0.108.0.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.47.2.0','0.4.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.108.1.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.108.0.0']),
% 3.57/3.99 [weight('<9,47,4,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.108.2.0',plain,
% 3.57/3.99 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_106]).
% 3.57/3.99 cnf('0.111.0.0',plain,
% 3.57/3.99 ( join(join(X1,X2),X3) = join(meet(X2,X4),join(join(X1,X2),X3)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.48.2.0','0.45.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.111.0.1',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(meet(X2,X4),join(join(X1,X2),X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.111.0.0','0.11.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.111.0.2',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(meet(X2,X4),join(X1,join(X2,X3))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.111.0.1','0.11.2.0',theory(equality)]),
% 3.57/3.99 [pos('R.2','L')]).
% 3.57/3.99 cnf('0.111.1.0',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(meet(X2,X4),join(X1,join(X2,X3))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.111.0.2']),
% 3.57/3.99 [weight('<9,48,45,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.111.2.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),join(X3,join(X1,X4))) = join(X3,join(X1,X4)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.111.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_109]).
% 3.57/3.99 cnf('0.114.0.0',plain,
% 3.57/3.99 ( join(join(X1,X2),X3) = join(meet(X1,X4),join(X3,join(X1,X2))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.50.2.0','0.43.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.114.0.1',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X3,join(X1,X2))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.114.0.0','0.11.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.114.1.0',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(meet(X1,X4),join(X3,join(X1,X2))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.114.0.1']),
% 3.57/3.99 [weight('<9,50,43,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.114.1.1',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.114.1.0','0.111.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.114.2.0',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 3.57/3.99 inference(activate,[status(thm)],['0.114.1.1']),
% 3.57/3.99 [equation_4]).
% 3.57/3.99 cnf('0.115.0.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),meet(X2,X3))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.56.2.0','0.4.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.1','L')]).
% 3.57/3.99 cnf('0.115.1.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),meet(X2,X3))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.115.0.0']),
% 3.57/3.99 [weight('<9,56,4,[1,0,0,1]>')]).
% 3.57/3.99 cnf('0.115.2.0',plain,
% 3.57/3.99 ( meet(X1,join(meet(X2,X1),meet(X1,X3))) = join(meet(X2,X1),meet(X1,X3)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.115.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_111]).
% 3.57/3.99 cnf('0.133.0.0',plain,
% 3.57/3.99 ( join(join(X1,meet(X2,X3)),join(X4,X2)) = join(X4,join(X2,X1)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.114.2.0','0.32.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.133.0.1',plain,
% 3.57/3.99 ( join(X1,join(meet(X2,X3),join(X4,X2))) = join(X4,join(X2,X1)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.133.0.0','0.11.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.133.1.0',plain,
% 3.57/3.99 ( join(X1,join(meet(X2,X3),join(X4,X2))) = join(X4,join(X2,X1)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.133.0.1']),
% 3.57/3.99 [weight('<9,114,32,[1,0,0,2]>')]).
% 3.57/3.99 cnf('0.133.1.1',plain,
% 3.57/3.99 ( join(X1,join(X2,join(meet(X2,X3),X4))) = join(X4,join(X2,X1)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.133.1.0','0.114.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.133.1.2',plain,
% 3.57/3.99 ( join(X1,join(X2,X4)) = join(X4,join(X2,X1)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.133.1.1','0.19.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.133.2.0',plain,
% 3.57/3.99 ( join(X1,join(X2,X3)) = join(X3,join(X2,X1)) ),
% 3.57/3.99 inference(activate,[status(thm)],['0.133.1.2']),
% 3.57/3.99 [equation_6]).
% 3.57/3.99 cnf('0.135.0.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.97.2.0','0.115.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.135.1.0',plain,
% 3.57/3.99 ( meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.135.0.0']),
% 3.57/3.99 [weight('<9,115,97,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.135.2.0',plain,
% 3.57/3.99 ( meet(X1,join(meet(X2,X3),meet(X3,X1))) = meet(X1,X3) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.135.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_129]).
% 3.57/3.99 cnf('0.154.0.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.6.2.0','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.154.1.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.154.0.0']),
% 3.57/3.99 [weight('<10,6,5,[1,0,0,0]>')]).
% 3.57/3.99 cnf('0.154.2.0',plain,
% 3.57/3.99 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 3.57/3.99 inference(activate,[status(thm)],['0.154.1.0']),
% 3.57/3.99 [equation_7]).
% 3.57/3.99 cnf('0.953.0.0',plain,
% 3.57/3.99 ( join(meet(X1,join(X2,meet(X3,X1))),meet(X2,join(X3,X1))) = meet(join(X2,meet(X3,X1)),join(X1,meet(X2,X3))) ),
% 3.57/3.99 inference(interreduction_right,[status(thm)],['0.8.2.0'])).
% 3.57/3.99 cnf('0.953.1.0',plain,
% 3.57/3.99 ( join(meet(X1,join(X2,meet(X3,X1))),meet(X2,join(X3,X1))) = meet(join(X2,meet(X3,X1)),join(X1,meet(X2,X3))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.953.0.0']),
% 3.57/3.99 [weight('<13,8,10,[0,0,0,0]>')]).
% 3.57/3.99 cnf('0.953.1.1',plain,
% 3.57/3.99 ( join(meet(X2,join(X3,X1)),meet(X1,join(X2,meet(X3,X1)))) = meet(join(X2,meet(X3,X1)),join(X1,meet(X2,X3))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.953.1.0','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.953.2.0',plain,
% 3.57/3.99 ( join(meet(X1,join(X2,X3)),meet(X3,join(X1,meet(X2,X3)))) = meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.953.1.1',theory(equality)]),
% 3.57/3.99 [u,rule_945]).
% 3.57/3.99 cnf('0.954.0.0',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = meet(meet(X1,join(X2,X3)),meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2)))) ),
% 3.57/3.99 inference(cp,[status(thm)],['0.2.2.0','0.953.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('0.954.0.1',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X3),meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.954.0.0','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.954.0.2',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = meet(X1,meet(join(X2,X3),join(X3,meet(X1,X2)))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.954.0.1','0.76.2.0',theory(equality)]),
% 3.57/3.99 [pos('R','L')]).
% 3.57/3.99 cnf('0.954.0.3',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = meet(X1,join(X3,meet(X1,X2))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.954.0.2','0.88.2.0',theory(equality)]),
% 3.57/3.99 [pos('R.2','L')]).
% 3.57/3.99 cnf('0.954.1.0',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = meet(X1,join(X3,meet(X1,X2))) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.954.0.3']),
% 3.57/3.99 [weight('<7,953,2,[0,0,0,2]>')]).
% 3.57/3.99 cnf('0.954.2.0',plain,
% 3.57/3.99 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.954.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_946]).
% 3.57/3.99 cnf('0.955.0.0',plain,
% 3.57/3.99 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)) ),
% 3.57/3.99 inference(interreduction_right,[status(thm)],['0.108.2.0'])).
% 3.57/3.99 cnf('0.955.0.1',plain,
% 3.57/3.99 ( meet(X1,join(X3,meet(X1,X2))) = join(meet(X1,X2),meet(X1,X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.955.0.0','0.954.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.955.0.2',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)) ),
% 3.57/3.99 inference(reduction,[status(thm)],['0.955.0.1','0.954.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('0.955.1.0',plain,
% 3.57/3.99 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)) ),
% 3.57/3.99 inference(weigh,[status(thm)],['0.955.0.2']),
% 3.57/3.99 [weight('<7,108,954,[0,0,0,0]>')]).
% 3.57/3.99 cnf('0.955.2.0',plain,
% 3.57/3.99 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)) ),
% 3.57/3.99 inference(orient,[status(thm)],['0.955.1.0',theory(equality)]),
% 3.57/3.99 [x,rule_947]).
% 3.57/3.99 cnf('1.0.0.0',conjecture,
% 3.57/3.99 ( meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 file('/tmp/WALDMEISTER_26737_n011',conjecture_1)).
% 3.57/3.99 cnf('1.0.0.1',plain,
% 3.57/3.99 ( meet(a,meet(meet(join(b,c),join(b,d)),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.0','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('1.0.0.2',plain,
% 3.57/3.99 ( meet(a,meet(join(b,c),meet(join(b,d),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.1','0.6.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('1.0.0.3',plain,
% 3.57/3.99 ( meet(a,meet(join(b,d),meet(join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d))),join(b,c)))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.2','0.154.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','R')]).
% 3.57/3.99 cnf('1.0.0.4',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d))),join(b,c)))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.3','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.1','L')]).
% 3.57/3.99 cnf('1.0.0.5',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(b,c),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.4','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.6',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(c,b),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.5','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2.1','L')]).
% 3.57/3.99 cnf('1.0.0.7',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(c,b),join(meet(a,d),join(meet(a,c),meet(a,join(b,meet(c,d)))))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.6','0.133.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.8',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(c,b),join(meet(d,a),join(meet(a,c),meet(a,join(b,meet(c,d)))))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.7','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2.2.1','L')]).
% 3.57/3.99 cnf('1.0.0.9',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(c,b),join(meet(d,a),meet(a,join(c,join(b,meet(c,d)))))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.8','0.955.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.10',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(c,b),join(meet(d,a),meet(a,join(c,b)))))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.9','0.32.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2.2.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.11',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(join(c,b),a))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.10','0.135.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.12',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),meet(a,join(c,b)))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.11','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.13',plain,
% 3.57/3.99 ( meet(a,meet(a,meet(join(c,b),join(d,b)))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.12','0.154.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','R')]).
% 3.57/3.99 cnf('1.0.0.14',plain,
% 3.57/3.99 ( meet(a,meet(join(c,b),join(d,b))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.13','0.13.2.0',theory(equality)]),
% 3.57/3.99 [pos('L','L')]).
% 3.57/3.99 cnf('1.0.0.15',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),join(c,b))) = meet(a,meet(join(b,c),join(b,d))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.14','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('L.2','L')]).
% 3.57/3.99 cnf('1.0.0.16',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),join(c,b))) = meet(a,meet(join(b,d),join(b,c))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.15','0.5.2.0',theory(equality)]),
% 3.57/3.99 [pos('R.2','L')]).
% 3.57/3.99 cnf('1.0.0.17',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),join(c,b))) = meet(a,meet(join(d,b),join(b,c))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.16','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('R.2.1','L')]).
% 3.57/3.99 cnf('1.0.0.18',plain,
% 3.57/3.99 ( meet(a,meet(join(d,b),join(c,b))) = meet(a,meet(join(d,b),join(c,b))) ),
% 3.57/3.99 inference(reduction,[status(thm)],['1.0.0.17','0.10.2.0',theory(equality)]),
% 3.57/3.99 [pos('R.2.2','L')]).
% 3.57/3.99 cnf('1.0.0.19',plain,
% 3.57/3.99 ( $true ),
% 3.57/3.99 inference(trivial,[status(thm)],['1.0.0.18',theory(equality)]),
% 3.57/3.99 [conjecture_1]).
% 3.57/3.99
% 3.57/3.99 Proved Goals:
% 3.57/3.99 No. 1: meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))) ?= meet(a,meet(join(b,c),join(b,d))) joined, current: meet(a,meet(join(d,b),join(c,b))) = meet(a,meet(join(d,b),join(c,b)))
% 3.57/3.99 1 goal was specified, which was proved.
% 3.57/3.99 % SZS output end CNFRefutation
% 3.57/3.99 #END OF PROOF
% 3.57/3.99
% 3.57/3.99 Problem WALDMEISTER_26737_n011
% 3.57/3.99 CPs.gen 852130
% 3.57/3.99 CPs.reexp 0
% 3.57/3.99 Select 30058
% 3.57/3.99 R 947
% 3.57/3.99 E 8
% 3.57/3.99 vsize 8.6M
% 3.57/3.99 rss 4.2M
% 3.57/3.99 process.time 2.984s
% 3.57/3.99 wallclock.time 2.984s
% 3.57/3.99 status S
% 3.57/3.99
% 3.57/3.99
% 3.57/3.99 Waldmeister states: Goal proved.
% 3.57/3.99 % SZS status Unsatisfiable
%------------------------------------------------------------------------------