TSTP Solution File: LAT005-10 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT005-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n012.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 07:14:35 EDT 2022
% Result : Unsatisfiable 20.37s 20.75s
% Output : CNFRefutation 20.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT005-10 : TPTP v8.1.0. Released v7.5.0.
% 0.00/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 03:35:48 EDT 2022
% 0.12/0.33 % 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) meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ?=? r1
% 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
% 20.37/20.75 joined goal: 1 meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ?= r1 to r1
% 20.37/20.75 goal joined
% 20.37/20.75 % SZS status Unsatisfiable
% 20.37/20.75 #START OF PROOF
% 20.37/20.75 % SZS output start CNFRefutation
% 20.37/20.75 cnf('0.1.0.0',axiom,
% 20.37/20.75 ( X1 = meet(X1,X1) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.1.1.0',plain,
% 20.37/20.75 ( X1 = meet(X1,X1) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.1.0.0']),
% 20.37/20.75 [weight('<0,0,0,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.1.2.0',plain,
% 20.37/20.75 ( meet(X1,X1) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_1]).
% 20.37/20.75 cnf('0.2.0.0',axiom,
% 20.37/20.75 ( X1 = meet(X1,join(X1,X2)) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.2.1.0',plain,
% 20.37/20.75 ( X1 = meet(X1,join(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.2.0.0']),
% 20.37/20.75 [weight('<1,0,0,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.2.2.0',plain,
% 20.37/20.75 ( meet(X1,join(X1,X2)) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_2]).
% 20.37/20.75 cnf('0.3.0.0',axiom,
% 20.37/20.75 ( X1 = meet(X1,n1) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.3.1.0',plain,
% 20.37/20.75 ( X1 = meet(X1,n1) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.3.0.0']),
% 20.37/20.75 [weight('<2,0,0,[0,0,0,3]>')]).
% 20.37/20.75 cnf('0.3.2.0',plain,
% 20.37/20.75 ( meet(X1,n1) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_3]).
% 20.37/20.75 cnf('0.5.0.0',axiom,
% 20.37/20.75 ( X1 = join(X1,meet(X1,X2)) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.5.1.0',plain,
% 20.37/20.75 ( X1 = join(X1,meet(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.5.0.0']),
% 20.37/20.75 [weight('<4,0,0,[0,0,0,5]>')]).
% 20.37/20.75 cnf('0.5.2.0',plain,
% 20.37/20.75 ( join(X1,meet(X1,X2)) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_5]).
% 20.37/20.75 cnf('0.6.0.0',axiom,
% 20.37/20.75 ( X1 = join(X1,n0) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.6.1.0',plain,
% 20.37/20.75 ( X1 = join(X1,n0) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.6.0.0']),
% 20.37/20.75 [weight('<5,0,0,[0,0,0,6]>')]).
% 20.37/20.75 cnf('0.6.2.0',plain,
% 20.37/20.75 ( join(X1,n0) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_6]).
% 20.37/20.75 cnf('0.7.0.0',axiom,
% 20.37/20.75 ( X1 = ifeq(X2,X2,X1,X3) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.7.1.0',plain,
% 20.37/20.75 ( X1 = ifeq(X2,X2,X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.7.0.0']),
% 20.37/20.75 [weight('<6,0,0,[0,0,0,7]>')]).
% 20.37/20.75 cnf('0.7.2.0',plain,
% 20.37/20.75 ( ifeq(X1,X1,X2,X3) = X2 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_7]).
% 20.37/20.75 cnf('0.9.0.0',axiom,
% 20.37/20.75 ( X1 = ifeq3(X2,X2,X1,X3) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.9.1.0',plain,
% 20.37/20.75 ( X1 = ifeq3(X2,X2,X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.9.0.0']),
% 20.37/20.75 [weight('<8,0,0,[0,0,0,9]>')]).
% 20.37/20.75 cnf('0.9.2.0',plain,
% 20.37/20.75 ( ifeq3(X1,X1,X2,X3) = X2 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_9]).
% 20.37/20.75 cnf('0.10.0.0',axiom,
% 20.37/20.75 ( meet(X1,X2) = meet(X2,X1) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.10.1.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(X2,X1) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.10.0.0']),
% 20.37/20.75 [weight('<9,0,0,[0,0,0,10]>')]).
% 20.37/20.75 cnf('0.10.2.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(X2,X1) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.10.1.0']),
% 20.37/20.75 [equation_1]).
% 20.37/20.75 cnf('0.11.0.0',axiom,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.11.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.11.0.0']),
% 20.37/20.75 [weight('<10,0,0,[0,0,0,11]>')]).
% 20.37/20.75 cnf('0.11.2.0',plain,
% 20.37/20.75 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_10]).
% 20.37/20.75 cnf('0.13.0.0',axiom,
% 20.37/20.75 ( join(X1,X2) = join(X2,X1) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.13.1.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(X2,X1) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.13.0.0']),
% 20.37/20.75 [weight('<12,0,0,[0,0,0,13]>')]).
% 20.37/20.75 cnf('0.13.2.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(X2,X1) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.13.1.0']),
% 20.37/20.75 [equation_2]).
% 20.37/20.75 cnf('0.14.0.0',axiom,
% 20.37/20.75 ( join(X1,meet(X2,X3)) = ifeq3(meet(X1,X3),X1,meet(X3,join(X1,X2)),join(X1,meet(X2,X3))) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.14.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,X3)) = ifeq3(meet(X1,X3),X1,meet(X3,join(X1,X2)),join(X1,meet(X2,X3))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.14.0.0']),
% 20.37/20.75 [weight('<13,0,0,[0,0,0,14]>')]).
% 20.37/20.75 cnf('0.14.2.0',plain,
% 20.37/20.75 ( ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_12]).
% 20.37/20.75 cnf('0.15.0.0',axiom,
% 20.37/20.75 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.15.1.0',plain,
% 20.37/20.75 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.15.0.0']),
% 20.37/20.75 [weight('<14,0,0,[0,0,0,15]>')]).
% 20.37/20.75 cnf('0.15.2.0',plain,
% 20.37/20.75 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_13]).
% 20.37/20.75 cnf('0.16.0.0',axiom,
% 20.37/20.75 ( join(X1,n1) = n1 ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.16.1.0',plain,
% 20.37/20.75 ( join(X1,n1) = n1 ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.16.0.0']),
% 20.37/20.75 [weight('<15,0,0,[0,0,0,16]>')]).
% 20.37/20.75 cnf('0.16.2.0',plain,
% 20.37/20.75 ( join(X1,n1) = n1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_14]).
% 20.37/20.75 cnf('0.17.0.0',axiom,
% 20.37/20.75 ( true = complement(r1,join(a,b)) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.17.1.0',plain,
% 20.37/20.75 ( true = complement(r1,join(a,b)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.17.0.0']),
% 20.37/20.75 [weight('<16,0,0,[0,0,0,17]>')]).
% 20.37/20.75 cnf('0.17.1.1',plain,
% 20.37/20.75 ( true = complement(r1,join(b,a)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.17.1.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.17.2.0',plain,
% 20.37/20.75 ( true = complement(r1,join(b,a)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.17.1.1',theory(equality)]),
% 20.37/20.75 [u,rule_15]).
% 20.37/20.75 cnf('0.18.0.0',axiom,
% 20.37/20.75 ( true = complement(r2,meet(a,b)) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.18.1.0',plain,
% 20.37/20.75 ( true = complement(r2,meet(a,b)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.18.0.0']),
% 20.37/20.75 [weight('<17,0,0,[0,0,0,18]>')]).
% 20.37/20.75 cnf('0.18.1.1',plain,
% 20.37/20.75 ( complement(r1,join(b,a)) = complement(r2,meet(a,b)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.18.1.0','0.17.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.18.1.2',plain,
% 20.37/20.75 ( complement(r1,join(b,a)) = complement(r2,meet(b,a)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.18.1.1','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.18.2.0',plain,
% 20.37/20.75 ( complement(r1,join(b,a)) = complement(r2,meet(b,a)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.18.1.2',theory(equality)]),
% 20.37/20.75 [u,rule_16]).
% 20.37/20.75 cnf('0.21.0.0',axiom,
% 20.37/20.75 ( n0 = ifeq(complement(X1,X2),true,meet(X1,X2),n0) ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012')).
% 20.37/20.75 cnf('0.21.1.0',plain,
% 20.37/20.75 ( n0 = ifeq(complement(X1,X2),true,meet(X1,X2),n0) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.21.0.0']),
% 20.37/20.75 [weight('<20,0,0,[0,0,0,21]>')]).
% 20.37/20.75 cnf('0.21.2.0',plain,
% 20.37/20.75 ( ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_19]).
% 20.37/20.75 cnf('0.22.0.0',plain,
% 20.37/20.75 ( true = complement(r1,join(b,a)) ),
% 20.37/20.75 inference(interreduction_right,[status(thm)],['0.17.2.0'])).
% 20.37/20.75 cnf('0.22.0.1',plain,
% 20.37/20.75 ( true = complement(r2,meet(b,a)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.22.0.0','0.18.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.22.1.0',plain,
% 20.37/20.75 ( true = complement(r2,meet(b,a)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.22.0.1']),
% 20.37/20.75 [weight('<1,17,18,[0,0,0,0]>')]).
% 20.37/20.75 cnf('0.22.2.0',plain,
% 20.37/20.75 ( true = complement(r2,meet(b,a)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_20]).
% 20.37/20.75 cnf('0.23.0.0',plain,
% 20.37/20.75 ( meet(n1,X1) = X1 ),
% 20.37/20.75 inference(cp,[status(thm)],['0.10.2.0','0.3.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.23.1.0',plain,
% 20.37/20.75 ( meet(n1,X1) = X1 ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.23.0.0']),
% 20.37/20.75 [weight('<3,10,3,[1,0,0,0]>')]).
% 20.37/20.75 cnf('0.23.2.0',plain,
% 20.37/20.75 ( meet(n1,X1) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_21]).
% 20.37/20.75 cnf('0.27.0.0',plain,
% 20.37/20.75 ( X1 = join(X1,meet(X2,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.5.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.27.1.0',plain,
% 20.37/20.75 ( X1 = join(X1,meet(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.27.0.0']),
% 20.37/20.75 [weight('<5,10,5,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.27.2.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,X1)) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_25]).
% 20.37/20.75 cnf('0.28.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.1.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.28.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.28.0.0']),
% 20.37/20.75 [weight('<5,11,1,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.28.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_26]).
% 20.37/20.75 cnf('0.29.0.0',plain,
% 20.37/20.75 ( X1 = meet(X1,join(X2,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.2.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.29.1.0',plain,
% 20.37/20.75 ( X1 = meet(X1,join(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.29.0.0']),
% 20.37/20.75 [weight('<5,13,2,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.29.2.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,X1)) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_27]).
% 20.37/20.75 cnf('0.33.0.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(join(X1,X2),X1) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.27.2.0','0.2.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.33.0.1',plain,
% 20.37/20.75 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.33.0.0','0.15.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.33.1.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.33.0.1']),
% 20.37/20.75 [weight('<5,27,2,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.33.2.0',plain,
% 20.37/20.75 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_31]).
% 20.37/20.75 cnf('0.34.0.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.28.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.34.1.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.34.0.0']),
% 20.37/20.75 [weight('<5,28,10,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.34.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X1)) = meet(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_32]).
% 20.37/20.75 cnf('0.35.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.2.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.35.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.35.0.0']),
% 20.37/20.75 [weight('<7,11,2,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.35.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_33]).
% 20.37/20.75 cnf('0.36.0.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = ifeq3(X1,X1,meet(join(X1,X3),join(X1,X2)),join(X1,meet(X2,join(X1,X3)))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.14.2.0','0.2.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.36.0.1',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.36.0.0','0.9.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.36.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.36.0.1']),
% 20.37/20.75 [weight('<7,14,2,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.36.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X3,join(X1,X2))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_34]).
% 20.37/20.75 cnf('0.37.0.0',plain,
% 20.37/20.75 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.15.2.0','0.5.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.37.1.0',plain,
% 20.37/20.75 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.37.0.0']),
% 20.37/20.75 [weight('<7,15,5,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.37.2.0',plain,
% 20.37/20.75 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_35]).
% 20.37/20.75 cnf('0.40.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.29.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.40.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.40.0.0']),
% 20.37/20.75 [weight('<7,29,11,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.40.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_38]).
% 20.37/20.75 cnf('0.41.0.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = ifeq3(X1,X1,meet(join(X3,X1),join(X1,X2)),join(X1,meet(X2,join(X3,X1)))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.14.2.0','0.29.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.41.0.1',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.41.0.0','0.9.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.41.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.41.0.1']),
% 20.37/20.75 [weight('<7,29,14,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.41.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(X3,join(X1,X2))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_39]).
% 20.37/20.75 cnf('0.45.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.34.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.45.0.1',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.45.0.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.45.0.2',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.45.0.1','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.45.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.45.0.2']),
% 20.37/20.75 [weight('<7,34,11,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.45.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_43]).
% 20.37/20.75 cnf('0.46.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X1,meet(X2,meet(X3,X1))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.34.2.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.46.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X1,meet(X2,meet(X3,X1))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.46.0.0']),
% 20.37/20.75 [weight('<7,34,11,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.46.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X3,X1))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_44]).
% 20.37/20.75 cnf('0.48.0.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X3))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.35.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.48.1.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X3))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.48.0.0']),
% 20.37/20.75 [weight('<7,35,10,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.48.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_46]).
% 20.37/20.75 cnf('0.49.0.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,join(X1,X3))) = meet(X1,join(X1,X3)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.35.2.0','0.29.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.49.0.1',plain,
% 20.37/20.75 ( meet(X1,join(X2,join(X1,X3))) = X1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.49.0.0','0.2.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.49.1.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,join(X1,X3))) = X1 ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.49.0.1']),
% 20.37/20.75 [weight('<7,35,29,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.49.2.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,join(X1,X3))) = X1 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_47]).
% 20.37/20.75 cnf('0.50.0.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X2,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.36.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.50.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.50.0.0']),
% 20.37/20.75 [weight('<7,36,13,[1,0,0,4]>')]).
% 20.37/20.75 cnf('0.50.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,join(X1,X2))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_48]).
% 20.37/20.75 cnf('0.51.0.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(X1,join(X2,meet(X1,X3))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.37.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.51.1.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(X1,join(X2,meet(X1,X3))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.51.0.0']),
% 20.37/20.75 [weight('<7,37,13,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.51.2.0',plain,
% 20.37/20.75 ( join(X1,join(X2,meet(X1,X3))) = join(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_49]).
% 20.37/20.75 cnf('0.55.0.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,join(X1,meet(X1,X2)))) = meet(X1,join(meet(X1,X2),X3)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.41.2.0','0.5.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.55.0.1',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(meet(X1,X2),X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.55.0.0','0.5.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('0.55.1.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(meet(X1,X2),X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.55.0.1']),
% 20.37/20.75 [weight('<7,41,5,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.55.2.0',plain,
% 20.37/20.75 ( meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X3,X1)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_53]).
% 20.37/20.75 cnf('0.56.0.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X1,X2),join(X3,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.41.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.56.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X1,X2),join(X3,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.56.0.0']),
% 20.37/20.75 [weight('<7,41,10,[1,0,0,0]>')]).
% 20.37/20.75 cnf('0.56.1.1',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,join(X1,X2))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.56.1.0','0.50.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.56.2.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,join(X1,X2))) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.56.1.1']),
% 20.37/20.75 [equation_3]).
% 20.37/20.75 cnf('0.58.0.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,join(X2,meet(X1,X2)))) = meet(X2,join(meet(X1,X2),X3)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.41.2.0','0.27.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.58.0.1',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.58.0.0','0.27.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('0.58.1.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.58.0.1']),
% 20.37/20.75 [weight('<7,41,27,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.58.2.0',plain,
% 20.37/20.75 ( meet(X1,join(meet(X2,X1),X3)) = join(meet(X2,X1),meet(X3,X1)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_55]).
% 20.37/20.75 cnf('0.59.0.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(X3,meet(X1,X2))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.55.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.59.1.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(X3,meet(X1,X2))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.59.0.0']),
% 20.37/20.75 [weight('<7,55,13,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.59.2.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,meet(X1,X3))) = join(meet(X1,X3),meet(X2,X1)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_56]).
% 20.37/20.75 cnf('0.60.0.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(join(X2,X1),X3)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.56.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.60.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(join(X2,X1),X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.60.0.0']),
% 20.37/20.75 [weight('<7,56,10,[1,0,0,2]>')]).
% 20.37/20.75 cnf('0.60.2.0',plain,
% 20.37/20.75 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X1,X3))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_57]).
% 20.37/20.75 cnf('0.61.0.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(join(X1,X2),X3)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.56.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.61.1.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(join(X1,X2),X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.61.0.0']),
% 20.37/20.75 [weight('<7,56,10,[1,1,0,2]>')]).
% 20.37/20.75 cnf('0.61.2.0',plain,
% 20.37/20.75 ( join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,join(X3,X1))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_58]).
% 20.37/20.75 cnf('0.63.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.2.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.63.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.63.0.0']),
% 20.37/20.75 [weight('<9,11,2,[1,0,0,0]>')]).
% 20.37/20.75 cnf('0.63.1.1',plain,
% 20.37/20.75 ( meet(X1,join(meet(X1,X2),meet(X3,X2))) = meet(X1,X2) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.63.1.0','0.58.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.63.1.2',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(meet(X3,X2),X1)) = meet(X1,X2) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.63.1.1','0.55.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.63.1.3',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,meet(X2,X1))) = meet(X1,X2) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.63.1.2','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.63.2.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,meet(X2,X1))) = meet(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.63.1.3',theory(equality)]),
% 20.37/20.75 [u,rule_60]).
% 20.37/20.75 cnf('0.66.0.0',plain,
% 20.37/20.75 ( join(X1,meet(n1,X2)) = ifeq3(meet(X1,X2),X1,meet(X2,join(X1,n1)),join(X1,X2)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.14.2.0','0.23.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.4.2','L')]).
% 20.37/20.75 cnf('0.66.0.1',plain,
% 20.37/20.75 ( join(X1,X2) = ifeq3(meet(X1,X2),X1,meet(X2,join(X1,n1)),join(X1,X2)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.66.0.0','0.23.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.66.0.2',plain,
% 20.37/20.75 ( join(X1,X2) = ifeq3(meet(X1,X2),X1,meet(X2,n1),join(X1,X2)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.66.0.1','0.16.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.3.2','L')]).
% 20.37/20.75 cnf('0.66.0.3',plain,
% 20.37/20.75 ( join(X1,X2) = ifeq3(meet(X1,X2),X1,X2,join(X1,X2)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.66.0.2','0.3.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.3','L')]).
% 20.37/20.75 cnf('0.66.1.0',plain,
% 20.37/20.75 ( join(X1,X2) = ifeq3(meet(X1,X2),X1,X2,join(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.66.0.3']),
% 20.37/20.75 [weight('<9,23,14,[0,0,0,12]>')]).
% 20.37/20.75 cnf('0.66.2.0',plain,
% 20.37/20.75 ( ifeq3(meet(X1,X2),X1,X2,join(X1,X2)) = join(X1,X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_63]).
% 20.37/20.75 cnf('0.68.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.27.2.0','0.35.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.68.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.68.0.0']),
% 20.37/20.75 [weight('<9,35,27,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.68.1.1',plain,
% 20.37/20.75 ( meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.68.1.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.68.2.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.68.1.1',theory(equality)]),
% 20.37/20.75 [x,rule_65]).
% 20.37/20.75 cnf('0.69.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X1,X3)) = join(meet(X1,X3),meet(join(X1,X2),meet(X1,X3))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.68.2.0','0.28.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.69.0.1',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.69.0.0','0.27.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.69.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.69.0.1']),
% 20.37/20.75 [weight('<7,68,28,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.69.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_66]).
% 20.37/20.75 cnf('0.70.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,X1)) = join(meet(X1,X3),meet(join(X1,X2),meet(X3,X1))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.68.2.0','0.34.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.70.0.1',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,X1)) = meet(X1,X3) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.70.0.0','0.63.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.70.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,X1)) = meet(X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.70.0.1']),
% 20.37/20.75 [weight('<7,68,34,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.70.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,X1)) = meet(X1,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_67]).
% 20.37/20.75 cnf('0.71.0.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(join(X3,X1),meet(X1,X2)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.69.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.71.1.0',plain,
% 20.37/20.75 ( meet(X1,X2) = meet(join(X3,X1),meet(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.71.0.0']),
% 20.37/20.75 [weight('<7,69,13,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.71.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X2,X3)) = meet(X2,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_68]).
% 20.37/20.75 cnf('0.73.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,X3),X4)) = meet(join(X1,meet(X3,join(X1,X2))),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.36.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.73.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,X3),X4)) = meet(join(X1,meet(X3,join(X1,X2))),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.73.0.0']),
% 20.37/20.75 [weight('<9,36,11,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.73.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,join(X1,X3))),X4) = meet(join(X1,X3),meet(join(X1,X2),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_70]).
% 20.37/20.75 cnf('0.84.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,X3),X4)) = meet(join(X2,meet(X3,join(X1,X2))),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.41.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.84.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,X3),X4)) = meet(join(X2,meet(X3,join(X1,X2))),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.84.0.0']),
% 20.37/20.75 [weight('<9,41,11,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.84.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,join(X3,X1))),X4) = meet(join(X3,X1),meet(join(X1,X2),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.84.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_81]).
% 20.37/20.75 cnf('0.101.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(join(X3,X1),X4))) = meet(X1,meet(join(X3,X1),meet(X2,X4))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.40.2.0','0.45.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.101.0.1',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(join(X3,X1),X4))) = meet(X1,meet(X2,X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.101.0.0','0.40.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.101.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(join(X3,X1),X4))) = meet(X1,meet(X2,X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.101.0.1']),
% 20.37/20.75 [weight('<9,45,40,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.101.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(join(X3,X1),X4))) = meet(X1,meet(X2,X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.101.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_98]).
% 20.37/20.75 cnf('0.104.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X3,join(X1,X4)))) = meet(X1,meet(join(X1,X4),meet(X2,X3))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.35.2.0','0.46.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.104.0.1',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X3,join(X1,X4)))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.104.0.0','0.35.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.104.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X3,join(X1,X4)))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.104.0.1']),
% 20.37/20.75 [weight('<9,46,35,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.104.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(X3,join(X1,X4)))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.104.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_101]).
% 20.37/20.75 cnf('0.107.0.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X2,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.27.2.0','0.48.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.107.1.0',plain,
% 20.37/20.75 ( meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.107.0.0']),
% 20.37/20.75 [weight('<9,48,27,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.107.1.1',plain,
% 20.37/20.75 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X2,X3))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.107.1.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.107.2.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.107.1.1',theory(equality)]),
% 20.37/20.75 [x,rule_104]).
% 20.37/20.75 cnf('0.117.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(join(meet(X1,X2),meet(X3,X1)),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.55.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.117.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(join(meet(X1,X2),meet(X3,X1)),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.117.0.0']),
% 20.37/20.75 [weight('<9,55,11,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.117.2.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X3,X1)),X4) = meet(X1,meet(join(meet(X1,X2),X3),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.117.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_114]).
% 20.37/20.75 cnf('0.124.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X2,X1),X3),X4)) = meet(join(meet(X2,X1),meet(X3,X1)),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.11.2.0','0.58.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.124.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X2,X1),X3),X4)) = meet(join(meet(X2,X1),meet(X3,X1)),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.124.0.0']),
% 20.37/20.75 [weight('<9,58,11,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.124.2.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X3,X2)),X4) = meet(X2,meet(join(meet(X1,X2),X3),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_120]).
% 20.37/20.75 cnf('0.139.0.0',plain,
% 20.37/20.75 ( join(X1,X2) = ifeq3(meet(X2,X1),X1,X2,join(X1,X2)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.66.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.139.1.0',plain,
% 20.37/20.75 ( join(X1,X2) = ifeq3(meet(X2,X1),X1,X2,join(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.139.0.0']),
% 20.37/20.75 [weight('<9,66,10,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.139.2.0',plain,
% 20.37/20.75 ( ifeq3(meet(X1,X2),X2,X1,join(X2,X1)) = join(X2,X1) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_135]).
% 20.37/20.75 cnf('0.140.0.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),join(X1,X3)) = ifeq3(meet(X1,X2),meet(X1,X2),join(X1,X3),join(meet(X1,X2),join(X1,X3))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.139.2.0','0.69.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.140.0.1',plain,
% 20.37/20.75 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.140.0.0','0.9.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.140.1.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.140.0.1']),
% 20.37/20.75 [weight('<7,139,69,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.140.2.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.140.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_136]).
% 20.37/20.75 cnf('0.142.0.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(meet(X3,X1),join(X1,X2)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.140.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.142.1.0',plain,
% 20.37/20.75 ( join(X1,X2) = join(meet(X3,X1),join(X1,X2)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.142.0.0']),
% 20.37/20.75 [weight('<7,140,10,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.142.2.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),join(X2,X3)) = join(X2,X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_138]).
% 20.37/20.75 cnf('0.149.0.0',plain,
% 20.37/20.75 ( join(meet(join(X1,X2),meet(X1,X3)),meet(X4,join(X1,X2))) = meet(join(X1,X2),join(X4,meet(X1,X3))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.59.2.0','0.69.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('0.149.0.1',plain,
% 20.37/20.75 ( join(meet(X1,X3),meet(X4,join(X1,X2))) = meet(join(X1,X2),join(X4,meet(X1,X3))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.149.0.0','0.69.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.149.1.0',plain,
% 20.37/20.75 ( join(meet(X1,X3),meet(X4,join(X1,X2))) = meet(join(X1,X2),join(X4,meet(X1,X3))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.149.0.1']),
% 20.37/20.75 [weight('<9,69,59,[0,0,0,4]>')]).
% 20.37/20.75 cnf('0.149.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),join(X3,meet(X1,X4))) = join(meet(X1,X4),meet(X3,join(X1,X2))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.149.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_144]).
% 20.37/20.75 cnf('0.151.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(join(X1,X4),meet(X2,meet(X3,X1))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.70.2.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.151.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(join(X1,X4),meet(X2,meet(X3,X1))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.151.0.0']),
% 20.37/20.75 [weight('<9,70,11,[1,0,0,4]>')]).
% 20.37/20.75 cnf('0.151.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,meet(X4,X1))) = meet(X1,meet(X3,X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.151.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_146]).
% 20.37/20.75 cnf('0.153.0.0',plain,
% 20.37/20.75 ( join(meet(join(X1,X2),meet(X2,X3)),meet(X4,join(X1,X2))) = meet(join(X1,X2),join(meet(X2,X3),X4)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.55.2.0','0.71.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.1','L')]).
% 20.37/20.75 cnf('0.153.0.1',plain,
% 20.37/20.75 ( join(meet(X2,X3),meet(X4,join(X1,X2))) = meet(join(X1,X2),join(meet(X2,X3),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.153.0.0','0.71.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.153.1.0',plain,
% 20.37/20.75 ( join(meet(X2,X3),meet(X4,join(X1,X2))) = meet(join(X1,X2),join(meet(X2,X3),X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.153.0.1']),
% 20.37/20.75 [weight('<9,71,55,[0,0,0,3]>')]).
% 20.37/20.75 cnf('0.153.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),join(meet(X2,X3),X4)) = join(meet(X2,X3),meet(X4,join(X1,X2))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_148]).
% 20.37/20.75 cnf('0.166.0.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X1,X2)),meet(join(meet(X1,X2),X2),X3)) = meet(meet(X2,join(X1,meet(X1,X2))),X3) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.84.2.0','0.107.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.166.0.1',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X2),X3)) = meet(meet(X2,join(X1,meet(X1,X2))),X3) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.166.0.0','0.5.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.166.0.2',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X2),X3)) = meet(X2,meet(join(X1,meet(X1,X2)),X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.166.0.1','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.166.0.3',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X2),X3)) = meet(X2,meet(X1,X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.166.0.2','0.5.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2.1','L')]).
% 20.37/20.75 cnf('0.166.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X2),X3)) = meet(X2,meet(X1,X3)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.166.0.3']),
% 20.37/20.75 [weight('<9,107,84,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.166.1.1',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,meet(X1,X2)),X3)) = meet(X2,meet(X1,X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.166.1.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.1','L')]).
% 20.37/20.75 cnf('0.166.1.2',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.166.1.1','0.27.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.1','L')]).
% 20.37/20.75 cnf('0.166.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.166.1.2']),
% 20.37/20.75 [equation_6]).
% 20.37/20.75 cnf('0.171.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(join(meet(X3,X1),meet(X1,X2)),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.117.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.171.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(join(meet(X3,X1),meet(X1,X2)),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.171.0.0']),
% 20.37/20.75 [weight('<9,117,13,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.171.2.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X2,X3)),X4) = meet(X2,meet(join(meet(X2,X3),X1),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.171.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_163]).
% 20.37/20.75 cnf('0.176.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X2,X1),X3),X4)) = meet(join(meet(X2,X1),meet(X1,X3)),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.124.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2','L')]).
% 20.37/20.75 cnf('0.176.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X2,X1),X3),X4)) = meet(join(meet(X2,X1),meet(X1,X3)),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.176.0.0']),
% 20.37/20.75 [weight('<9,124,10,[1,0,0,5]>')]).
% 20.37/20.75 cnf('0.176.1.1',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X2,X1),X3),X4)) = meet(X1,meet(join(meet(X1,X3),X2),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.176.1.0','0.171.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.176.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X2,X1),X3),X4)) = meet(X1,meet(join(meet(X1,X3),X2),X4)) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.176.1.1']),
% 20.37/20.75 [equation_11]).
% 20.37/20.75 cnf('0.186.0.0',plain,
% 20.37/20.75 ( meet(meet(X1,X2),X3) = meet(join(X2,X4),meet(X3,meet(X1,X2))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.70.2.0','0.142.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.186.0.1',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(join(X2,X4),meet(X3,meet(X1,X2))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.186.0.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.186.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(join(X2,X4),meet(X3,meet(X1,X2))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.186.0.1']),
% 20.37/20.75 [weight('<9,142,70,[0,0,0,1]>')]).
% 20.37/20.75 cnf('0.186.1.1',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.186.1.0','0.151.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.186.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.186.1.1']),
% 20.37/20.75 [equation_12]).
% 20.37/20.75 cnf('0.194.0.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,join(X1,X4))) = meet(join(X3,meet(X1,X2)),join(X1,X4)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.149.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.194.1.0',plain,
% 20.37/20.75 ( join(meet(X1,X2),meet(X3,join(X1,X4))) = meet(join(X3,meet(X1,X2)),join(X1,X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.194.0.0']),
% 20.37/20.75 [weight('<9,149,10,[1,0,0,0]>')]).
% 20.37/20.75 cnf('0.194.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,X3)),join(X2,X4)) = join(meet(X2,X3),meet(X1,join(X2,X4))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.194.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_182]).
% 20.37/20.75 cnf('0.201.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(X1,meet(join(X2,meet(X3,X1)),X4)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.176.2.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.1','L')]).
% 20.37/20.75 cnf('0.201.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(X1,meet(join(X2,meet(X3,X1)),X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.201.0.0']),
% 20.37/20.75 [weight('<9,176,13,[1,0,0,3]>')]).
% 20.37/20.75 cnf('0.201.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(meet(X1,X2),X3),X4)) = meet(X1,meet(join(X2,meet(X3,X1)),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.201.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_188]).
% 20.37/20.75 cnf('0.204.0.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X2,X3)),X4) = meet(X2,meet(join(meet(X2,X3),X1),X4)) ),
% 20.37/20.75 inference(interreduction_right,[status(thm)],['0.171.2.0'])).
% 20.37/20.75 cnf('0.204.0.1',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X2,X3)),X4) = meet(X2,meet(join(X3,meet(X1,X2)),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.204.0.0','0.201.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.204.1.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X2,X3)),X4) = meet(X2,meet(join(X3,meet(X1,X2)),X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.204.0.1']),
% 20.37/20.75 [weight('<9,171,201,[0,0,0,0]>')]).
% 20.37/20.75 cnf('0.204.2.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X2,X3)),X4) = meet(X2,meet(join(X3,meet(X1,X2)),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.204.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_191]).
% 20.37/20.75 cnf('0.208.0.0',plain,
% 20.37/20.75 ( meet(meet(X1,join(X2,X3)),meet(X4,X2)) = meet(X4,meet(X2,X1)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.186.2.0','0.48.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.208.0.1',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,X3),meet(X4,X2))) = meet(X4,meet(X2,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.208.0.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.208.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,X3),meet(X4,X2))) = meet(X4,meet(X2,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.208.0.1']),
% 20.37/20.75 [weight('<9,186,48,[1,1,0,2]>')]).
% 20.37/20.75 cnf('0.208.1.1',plain,
% 20.37/20.75 ( meet(X1,meet(X2,meet(join(X2,X3),X4))) = meet(X4,meet(X2,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.208.1.0','0.186.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','R')]).
% 20.37/20.75 cnf('0.208.1.2',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X4)) = meet(X4,meet(X2,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.208.1.1','0.35.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.208.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.208.1.2']),
% 20.37/20.75 [equation_14]).
% 20.37/20.75 cnf('0.257.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,meet(X3,X4)),X5)) = meet(join(X1,meet(X3,meet(X4,join(X1,X2)))),X5) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.73.2.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2','L')]).
% 20.37/20.75 cnf('0.257.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,meet(X3,X4)),X5)) = meet(join(X1,meet(X3,meet(X4,join(X1,X2)))),X5) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.257.0.0']),
% 20.37/20.75 [weight('<11,73,11,[1,0,0,3]>')]).
% 20.37/20.75 cnf('0.257.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,meet(X3,join(X1,X4)))),X5) = meet(join(X1,X4),meet(join(X1,meet(X2,X3)),X5)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.257.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_235]).
% 20.37/20.75 cnf('0.260.0.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,X3)),meet(join(X1,X2),X4)) = meet(join(X1,join(meet(X2,X3),meet(X1,X2))),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.73.2.0','0.59.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2','L')]).
% 20.37/20.75 cnf('0.260.0.1',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,X3)),meet(join(X1,X2),X4)) = meet(join(X1,meet(X2,X3)),X4) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.260.0.0','0.51.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.1','L')]).
% 20.37/20.75 cnf('0.260.1.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,X3)),meet(join(X1,X2),X4)) = meet(join(X1,meet(X2,X3)),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.260.0.1']),
% 20.37/20.75 [weight('<11,73,59,[1,0,0,3]>')]).
% 20.37/20.75 cnf('0.260.1.1',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X4,join(X1,meet(X2,X3)))) = meet(join(X1,meet(X2,X3)),X4) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.260.1.0','0.186.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.260.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,join(X1,meet(X2,X4)))) = meet(join(X1,meet(X2,X4)),X3) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.260.1.1',theory(equality)]),
% 20.37/20.75 [u,rule_238]).
% 20.37/20.75 cnf('0.308.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,meet(X3,X4)),X5)) = meet(join(X2,meet(X3,meet(X4,join(X1,X2)))),X5) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.84.2.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2','L')]).
% 20.37/20.75 cnf('0.308.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,meet(X3,X4)),X5)) = meet(join(X2,meet(X3,meet(X4,join(X1,X2)))),X5) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.308.0.0']),
% 20.37/20.75 [weight('<11,84,11,[1,0,0,3]>')]).
% 20.37/20.75 cnf('0.308.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,meet(X3,join(X4,X1)))),X5) = meet(join(X4,X1),meet(join(X1,meet(X2,X3)),X5)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.308.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_286]).
% 20.37/20.75 cnf('0.366.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,X4)) = meet(join(X1,X2),meet(X3,meet(join(X2,X1),X4))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.101.2.0','0.33.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2.1','L')]).
% 20.37/20.75 cnf('0.366.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,X4)) = meet(join(X1,X2),meet(X3,meet(join(X2,X1),X4))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.366.0.0']),
% 20.37/20.75 [weight('<11,101,33,[1,0,0,5]>')]).
% 20.37/20.75 cnf('0.366.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(X3,meet(join(X2,X1),X4))) = meet(join(X1,X2),meet(X3,X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.366.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_342]).
% 20.37/20.75 cnf('0.378.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X1,meet(X2,join(meet(X3,X4),meet(X1,X3)))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.104.2.0','0.59.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('0.378.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,X3)) = meet(X1,meet(X2,join(meet(X3,X4),meet(X1,X3)))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.378.0.0']),
% 20.37/20.75 [weight('<11,104,59,[1,0,0,4]>')]).
% 20.37/20.75 cnf('0.378.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X3,X4),meet(X1,X3)))) = meet(X1,meet(X2,X3)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.378.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_354]).
% 20.37/20.75 cnf('0.379.0.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),X3),meet(X4,X1)) = meet(join(meet(X1,X2),X3),meet(X4,join(meet(X1,X2),meet(X3,join(X1,meet(X1,X2)))))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.378.2.0','0.61.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('0.379.0.1',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),X3),meet(X4,X1)) = meet(join(meet(X1,X2),meet(X3,join(X1,meet(X1,X2)))),X4) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.379.0.0','0.260.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.379.0.2',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),X3),meet(X4,X1)) = meet(join(X1,meet(X1,X2)),meet(join(meet(X1,X2),X3),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.379.0.1','0.84.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.379.0.3',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),X3),meet(X4,X1)) = meet(X1,meet(join(meet(X1,X2),X3),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.379.0.2','0.5.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.1','L')]).
% 20.37/20.75 cnf('0.379.0.4',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),X3),meet(X4,X1)) = meet(X1,meet(join(X2,meet(X3,X1)),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.379.0.3','0.201.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.379.1.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),X3),meet(X4,X1)) = meet(X1,meet(join(X2,meet(X3,X1)),X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.379.0.4']),
% 20.37/20.75 [weight('<9,378,61,[1,0,0,4]>')]).
% 20.37/20.75 cnf('0.379.1.1',plain,
% 20.37/20.75 ( meet(X1,meet(X4,join(meet(X1,X2),X3))) = meet(X1,meet(join(X2,meet(X3,X1)),X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.379.1.0','0.208.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.379.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X1,X3),X4))) = meet(X1,meet(join(X3,meet(X4,X1)),X2)) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.379.1.1']),
% 20.37/20.75 [equation_25]).
% 20.37/20.75 cnf('0.380.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X1,X3),X4))) = meet(X1,meet(X2,join(X3,meet(X4,X1)))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.379.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.380.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X1,X3),X4))) = meet(X1,meet(X2,join(X3,meet(X4,X1)))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.380.0.0']),
% 20.37/20.75 [weight('<9,379,10,[1,1,0,2]>')]).
% 20.37/20.75 cnf('0.380.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X1,X3),X4))) = meet(X1,meet(X2,join(X3,meet(X4,X1)))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.380.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_355]).
% 20.37/20.75 cnf('0.381.0.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(X3,meet(X4,X1)))) = meet(X1,meet(X2,join(meet(X3,X1),X4))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.380.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2.1','L')]).
% 20.37/20.75 cnf('0.381.1.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(X3,meet(X4,X1)))) = meet(X1,meet(X2,join(meet(X3,X1),X4))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.381.0.0']),
% 20.37/20.75 [weight('<9,380,10,[1,0,0,5]>')]).
% 20.37/20.75 cnf('0.381.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(X2,join(meet(X3,X1),X4))) = meet(X1,meet(X2,join(X3,meet(X4,X1)))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.381.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_356]).
% 20.37/20.75 cnf('0.495.0.0',plain,
% 20.37/20.75 ( meet(X1,join(meet(X2,X3),X4)) = meet(X1,join(meet(X2,X3),meet(X4,join(X1,X2)))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.35.2.0','0.153.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.495.1.0',plain,
% 20.37/20.75 ( meet(X1,join(meet(X2,X3),X4)) = meet(X1,join(meet(X2,X3),meet(X4,join(X1,X2)))) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.495.0.0']),
% 20.37/20.75 [weight('<11,153,35,[0,0,0,2]>')]).
% 20.37/20.75 cnf('0.495.2.0',plain,
% 20.37/20.75 ( meet(X1,join(meet(X2,X3),meet(X4,join(X1,X2)))) = meet(X1,join(meet(X2,X3),X4)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.495.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_463]).
% 20.37/20.75 cnf('0.560.0.0',plain,
% 20.37/20.75 ( join(meet(X1,meet(X2,X3)),meet(X4,join(X1,X5))) = meet(join(X4,meet(X2,meet(X1,X3))),join(X1,X5)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.194.2.0','0.166.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2','L')]).
% 20.37/20.75 cnf('0.560.1.0',plain,
% 20.37/20.75 ( join(meet(X1,meet(X2,X3)),meet(X4,join(X1,X5))) = meet(join(X4,meet(X2,meet(X1,X3))),join(X1,X5)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.560.0.0']),
% 20.37/20.75 [weight('<11,194,166,[1,0,0,3]>')]).
% 20.37/20.75 cnf('0.560.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,meet(X3,X4))),join(X3,X5)) = join(meet(X3,meet(X2,X4)),meet(X1,join(X3,X5))) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.560.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_518]).
% 20.37/20.75 cnf('0.670.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,meet(X3,X2)),X4)) = meet(join(X1,meet(X3,X2)),X4) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.257.2.0','0.29.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2.2','L')]).
% 20.37/20.75 cnf('0.670.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,meet(X3,X2)),X4)) = meet(join(X1,meet(X3,X2)),X4) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.670.0.0']),
% 20.37/20.75 [weight('<11,257,29,[1,0,0,5]>')]).
% 20.37/20.75 cnf('0.670.2.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X1,meet(X3,X2)),X4)) = meet(join(X1,meet(X3,X2)),X4) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.670.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_599]).
% 20.37/20.75 cnf('0.671.0.0',plain,
% 20.37/20.75 ( meet(join(meet(X1,X2),meet(X2,X3)),X4) = meet(join(meet(X1,X2),X3),meet(X2,meet(join(X3,meet(X1,X2)),X4))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.670.2.0','0.204.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.671.0.1',plain,
% 20.37/20.75 ( meet(X2,meet(join(X3,meet(X1,X2)),X4)) = meet(join(meet(X1,X2),X3),meet(X2,meet(join(X3,meet(X1,X2)),X4))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.671.0.0','0.204.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.671.0.2',plain,
% 20.37/20.75 ( meet(X2,meet(join(X3,meet(X1,X2)),X4)) = meet(join(meet(X1,X2),X3),meet(X2,X4)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.671.0.1','0.366.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.671.1.0',plain,
% 20.37/20.75 ( meet(X2,meet(join(X3,meet(X1,X2)),X4)) = meet(join(meet(X1,X2),X3),meet(X2,X4)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.671.0.2']),
% 20.37/20.75 [weight('<9,670,204,[1,0,0,4]>')]).
% 20.37/20.75 cnf('0.671.1.1',plain,
% 20.37/20.75 ( meet(X2,meet(join(X3,meet(X1,X2)),X4)) = meet(X2,meet(X4,join(meet(X1,X2),X3))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.671.1.0','0.186.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.671.1.2',plain,
% 20.37/20.75 ( meet(X2,meet(join(X3,meet(X1,X2)),X4)) = meet(X2,meet(X4,join(X1,meet(X3,X2)))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.671.1.1','0.381.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.671.2.0',plain,
% 20.37/20.75 ( meet(X1,meet(join(X2,meet(X3,X1)),X4)) = meet(X1,meet(X4,join(X3,meet(X2,X1)))) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.671.1.2']),
% 20.37/20.75 [equation_72]).
% 20.37/20.75 cnf('0.679.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,meet(X3,X4)),X5)) = meet(join(X2,meet(meet(X4,join(X1,X2)),X3)),X5) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.308.2.0','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1.2','L')]).
% 20.37/20.75 cnf('0.679.0.1',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,meet(X3,X4)),X5)) = meet(join(X2,meet(X4,meet(join(X1,X2),X3))),X5) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.679.0.0','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.1.2','L')]).
% 20.37/20.75 cnf('0.679.1.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,meet(X3,X4)),X5)) = meet(join(X2,meet(X4,meet(join(X1,X2),X3))),X5) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.679.0.1']),
% 20.37/20.75 [weight('<11,308,10,[1,0,0,3]>')]).
% 20.37/20.75 cnf('0.679.2.0',plain,
% 20.37/20.75 ( meet(join(X1,meet(X2,meet(join(X3,X1),X4))),X5) = meet(join(X3,X1),meet(join(X1,meet(X4,X2)),X5)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.679.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_606]).
% 20.37/20.75 cnf('0.680.0.0',plain,
% 20.37/20.75 ( meet(join(X1,X2),meet(join(X2,meet(X3,X4)),join(join(X1,X2),X5))) = join(meet(join(X1,X2),meet(X4,X3)),meet(X2,join(join(X1,X2),X5))) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.679.2.0','0.560.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.680.0.1',plain,
% 20.37/20.75 ( meet(join(X1,X2),join(X2,meet(X3,X4))) = join(meet(join(X1,X2),meet(X4,X3)),meet(X2,join(join(X1,X2),X5))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.0.0','0.48.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.680.0.2',plain,
% 20.37/20.75 ( join(X2,meet(meet(X3,X4),join(X1,X2))) = join(meet(join(X1,X2),meet(X4,X3)),meet(X2,join(join(X1,X2),X5))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.0.1','0.41.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.680.0.3',plain,
% 20.37/20.75 ( join(X2,meet(X3,meet(X4,join(X1,X2)))) = join(meet(join(X1,X2),meet(X4,X3)),meet(X2,join(join(X1,X2),X5))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.0.2','0.11.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.680.0.4',plain,
% 20.37/20.75 ( join(X2,meet(X3,meet(X4,join(X1,X2)))) = join(meet(join(X1,X2),meet(X4,X3)),meet(X2,join(X1,join(X2,X5)))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.0.3','0.15.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2.2','L')]).
% 20.37/20.75 cnf('0.680.0.5',plain,
% 20.37/20.75 ( join(X2,meet(X3,meet(X4,join(X1,X2)))) = join(meet(join(X1,X2),meet(X4,X3)),X2) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.0.4','0.49.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.680.1.0',plain,
% 20.37/20.75 ( join(X2,meet(X3,meet(X4,join(X1,X2)))) = join(meet(join(X1,X2),meet(X4,X3)),X2) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.680.0.5']),
% 20.37/20.75 [weight('<9,679,560,[1,0,0,0]>')]).
% 20.37/20.75 cnf('0.680.1.1',plain,
% 20.37/20.75 ( join(X2,meet(X3,meet(X4,join(X1,X2)))) = join(X2,meet(join(X1,X2),meet(X4,X3))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.1.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.680.1.2',plain,
% 20.37/20.75 ( join(X2,meet(X3,meet(X4,join(X1,X2)))) = join(X2,meet(X1,join(X2,meet(X4,X3)))) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.680.1.1','0.60.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.680.2.0',plain,
% 20.37/20.75 ( join(X1,meet(X2,meet(X3,join(X4,X1)))) = join(X1,meet(X4,join(X1,meet(X3,X2)))) ),
% 20.37/20.75 inference(activate,[status(thm)],['0.680.1.2']),
% 20.37/20.75 [equation_74]).
% 20.37/20.75 cnf('0.2622.0.0',plain,
% 20.37/20.75 ( ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0 ),
% 20.37/20.75 inference(interreduction_right,[status(thm)],['0.21.2.0'])).
% 20.37/20.75 cnf('0.2622.0.1',plain,
% 20.37/20.75 ( ifeq(complement(X1,X2),complement(r2,meet(b,a)),meet(X1,X2),n0) = n0 ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.2622.0.0','0.22.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.2622.1.0',plain,
% 20.37/20.75 ( ifeq(complement(X1,X2),complement(r2,meet(b,a)),meet(X1,X2),n0) = n0 ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.2622.0.1']),
% 20.37/20.75 [weight('<13,21,22,[0,0,0,0]>')]).
% 20.37/20.75 cnf('0.2622.2.0',plain,
% 20.37/20.75 ( ifeq(complement(X1,X2),complement(r2,meet(b,a)),meet(X1,X2),n0) = n0 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.2622.1.0',theory(equality)]),
% 20.37/20.75 [u,rule_2124]).
% 20.37/20.75 cnf('0.2623.0.0',plain,
% 20.37/20.75 ( n0 = meet(r2,meet(b,a)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.2622.2.0','0.7.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('0.2623.1.0',plain,
% 20.37/20.75 ( n0 = meet(r2,meet(b,a)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.2623.0.0']),
% 20.37/20.75 [weight('<5,2622,7,[1,0,0,0]>')]).
% 20.37/20.75 cnf('0.2623.2.0',plain,
% 20.37/20.75 ( meet(r2,meet(b,a)) = n0 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.2623.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_2125]).
% 20.37/20.75 cnf('0.2624.0.0',plain,
% 20.37/20.75 ( n0 = ifeq(complement(r2,meet(b,a)),complement(r2,meet(b,a)),meet(r1,join(b,a)),n0) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.2622.2.0','0.18.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.1','L')]).
% 20.37/20.75 cnf('0.2624.0.1',plain,
% 20.37/20.75 ( n0 = meet(r1,join(b,a)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.2624.0.0','0.7.2.0',theory(equality)]),
% 20.37/20.75 [pos('R','L')]).
% 20.37/20.75 cnf('0.2624.1.0',plain,
% 20.37/20.75 ( n0 = meet(r1,join(b,a)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.2624.0.1']),
% 20.37/20.75 [weight('<5,2622,18,[1,0,0,1]>')]).
% 20.37/20.75 cnf('0.2624.2.0',plain,
% 20.37/20.75 ( meet(r1,join(b,a)) = n0 ),
% 20.37/20.75 inference(orient,[status(thm)],['0.2624.1.0',theory(equality)]),
% 20.37/20.75 [x,rule_2126]).
% 20.37/20.75 cnf('0.2650.0.0',plain,
% 20.37/20.75 ( meet(b,join(meet(a,X1),r1)) = meet(b,join(meet(a,X1),n0)) ),
% 20.37/20.75 inference(cp,[status(thm)],['0.495.2.0','0.2624.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('0.2650.0.1',plain,
% 20.37/20.75 ( meet(b,join(meet(a,X1),r1)) = meet(b,meet(a,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.2650.0.0','0.6.2.0',theory(equality)]),
% 20.37/20.75 [pos('R.2','L')]).
% 20.37/20.75 cnf('0.2650.1.0',plain,
% 20.37/20.75 ( meet(b,join(meet(a,X1),r1)) = meet(b,meet(a,X1)) ),
% 20.37/20.75 inference(weigh,[status(thm)],['0.2650.0.1']),
% 20.37/20.75 [weight('<7,2624,495,[0,0,0,6]>')]).
% 20.37/20.75 cnf('0.2650.1.1',plain,
% 20.37/20.75 ( meet(b,join(r1,meet(a,X1))) = meet(b,meet(a,X1)) ),
% 20.37/20.75 inference(reduction,[status(thm)],['0.2650.1.0','0.13.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('0.2650.2.0',plain,
% 20.37/20.75 ( meet(b,join(r1,meet(a,X1))) = meet(b,meet(a,X1)) ),
% 20.37/20.75 inference(orient,[status(thm)],['0.2650.1.1',theory(equality)]),
% 20.37/20.75 [u,rule_2152]).
% 20.37/20.75 cnf('1.0.0.0',conjecture,
% 20.37/20.75 ( meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) = r1 ),
% 20.37/20.75 file('/tmp/WALDMEISTER_31059_n012',conjecture_1)).
% 20.37/20.75 cnf('1.0.0.1',plain,
% 20.37/20.75 ( join(r1,meet(meet(r2,a),join(r1,meet(r2,b)))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.0','0.36.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('1.0.0.2',plain,
% 20.37/20.75 ( join(r1,meet(b,meet(r2,join(meet(r2,a),r1)))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.1','0.680.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','R')]).
% 20.37/20.75 cnf('1.0.0.3',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(join(meet(r2,a),r1),b))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.2','0.186.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('1.0.0.4',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(join(a,meet(r1,r2)),b))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.3','0.201.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('1.0.0.5',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(b,join(r1,meet(a,r2))))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.4','0.671.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('1.0.0.6',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(b,meet(a,r2)))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.5','0.2650.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('1.0.0.7',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(r2,meet(a,b)))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.6','0.208.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('1.0.0.8',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(a,b))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.7','0.28.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('1.0.0.9',plain,
% 20.37/20.75 ( join(r1,meet(r2,meet(b,a))) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.8','0.10.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2.2','L')]).
% 20.37/20.75 cnf('1.0.0.10',plain,
% 20.37/20.75 ( join(r1,n0) = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.9','0.2623.2.0',theory(equality)]),
% 20.37/20.75 [pos('L.2','L')]).
% 20.37/20.75 cnf('1.0.0.11',plain,
% 20.37/20.75 ( r1 = r1 ),
% 20.37/20.75 inference(reduction,[status(thm)],['1.0.0.10','0.6.2.0',theory(equality)]),
% 20.37/20.75 [pos('L','L')]).
% 20.37/20.75 cnf('1.0.0.12',plain,
% 20.37/20.75 ( $true ),
% 20.37/20.75 inference(trivial,[status(thm)],['1.0.0.11',theory(equality)]),
% 20.37/20.75 [conjecture_1]).
% 20.37/20.75
% 20.37/20.75 Proved Goals:
% 20.37/20.75 No. 1: meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ?= r1 joined, current: r1 = r1
% 20.37/20.75 1 goal was specified, which was proved.
% 20.37/20.75 % SZS output end CNFRefutation
% 20.37/20.75 #END OF PROOF
% 20.37/20.75
% 20.37/20.75 Problem WALDMEISTER_31059_n012
% 20.37/20.75 CPs.gen 4064834
% 20.37/20.75 CPs.reexp 0
% 20.37/20.75 Select 218750
% 20.37/20.75 R 2152
% 20.37/20.75 E 498
% 20.37/20.75 vsize 10.8M
% 20.37/20.75 rss 6.2M
% 20.37/20.75 process.time 19.785s
% 20.37/20.75 wallclock.time 19.785s
% 20.37/20.75 status S
% 20.37/20.75
% 20.37/20.75
% 20.37/20.75 Waldmeister states: Goal proved.
% 20.37/20.75 % SZS status Unsatisfiable
%------------------------------------------------------------------------------