%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n021.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 07:14:37 EDT 2022
% Result : Unsatisfiable 0.64s 1.02s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : woody %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 28 22:19:11 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.64/0.99 ********************************************************************************
% 0.64/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.64/0.99 * |/ | \/ | *
% 0.64/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.64/0.99 * A. Jaeger and B. Loechner | | *
% 0.64/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.64/0.99 ********************************************************************************
% 0.64/0.99
% 0.64/0.99
% 0.64/0.99 Goals:
% 0.64/0.99 ------
% 0.64/0.99
% 0.64/0.99 ( 1) join(join(a,b),c) ?=? join(a,join(b,c))
% 0.64/0.99
% 0.64/0.99 Detected structure: Orkus
% 0.64/0.99 ********************************************************************************
% 0.64/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.64/0.99 ********************************************************************************
% 0.64/0.99
% 0.64/1.02 joined goal: 1 join(join(a,b),c) ?= join(a,join(b,c)) to join(join(c,b),a)
% 0.64/1.02 goal joined
% 0.64/1.02 % SZS status Unsatisfiable
% 0.64/1.02 #START OF PROOF
% 0.64/1.02 % SZS output start CNFRefutation
% 0.64/1.02 cnf('0.1.0.0',axiom,
% 0.64/1.02 ( X1 = meet(X1,join(X1,X2)) ),
% 0.64/1.02 file('/tmp/WALDMEISTER_8226_n021')).
% 0.64/1.02 cnf('0.1.1.0',plain,
% 0.64/1.02 ( X1 = meet(X1,join(X1,X2)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.64/1.02 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.64/1.02 cnf('0.1.2.0',plain,
% 0.64/1.02 ( meet(X1,join(X1,X2)) = X1 ),
% 0.64/1.02 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_1]).
% 0.64/1.02 cnf('0.2.0.0',axiom,
% 0.64/1.02 ( meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X2,X1)) ),
% 0.64/1.02 file('/tmp/WALDMEISTER_8226_n021')).
% 0.64/1.02 cnf('0.2.1.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X2,X1)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.64/1.02 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.64/1.02 cnf('0.2.2.0',plain,
% 0.64/1.02 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(X3,X1)) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_2]).
% 0.64/1.02 cnf('0.3.0.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.1','L')]).
% 0.64/1.02 cnf('0.3.1.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.64/1.02 [weight('<119,2,1,[1,0,0,1]>')]).
% 0.64/1.02 cnf('0.3.2.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_3]).
% 0.64/1.02 cnf('0.4.0.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X1,X3)) = join(meet(X3,join(X1,X2)),X1) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.4.1.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X1,X3)) = join(meet(X3,join(X1,X2)),X1) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.64/1.02 [weight('<119,2,1,[1,0,0,4]>')]).
% 0.64/1.02 cnf('0.4.2.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X1,X3)) = join(meet(X3,join(X1,X2)),X1) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_4]).
% 0.64/1.02 cnf('0.5.0.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,join(X3,X1))) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.1.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.5.1.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,join(X3,X1))) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.64/1.02 [weight('<129,2,1,[0,0,0,2]>')]).
% 0.64/1.02 cnf('0.5.2.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X1,X2) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_5]).
% 0.64/1.02 cnf('0.6.0.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(meet(X1,X2),X2) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.6.1.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(meet(X1,X2),X2) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.64/1.02 [weight('<53,5,1,[1,0,0,4]>')]).
% 0.64/1.02 cnf('0.6.2.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),X2) = meet(X1,X2) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_6]).
% 0.64/1.02 cnf('0.7.0.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,meet(X3,X1))) = join(meet(X3,X1),meet(X2,X1)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.6.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.1','L')]).
% 0.64/1.02 cnf('0.7.0.1',plain,
% 0.64/1.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.7.0.0','0.2.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.7.1.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.7.0.1']),
% 0.64/1.02 [weight('<103,6,2,[0,0,0,1]>')]).
% 0.64/1.02 cnf('0.7.2.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_7]).
% 0.64/1.02 cnf('0.8.0.0',plain,
% 0.64/1.02 ( meet(X1,join(meet(X2,X1),X3)) = join(meet(X3,X1),meet(X2,X1)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.6.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.8.0.1',plain,
% 0.64/1.02 ( meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.8.0.0','0.2.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.8.1.0',plain,
% 0.64/1.02 ( meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.8.0.1']),
% 0.64/1.02 [weight('<103,6,2,[0,0,0,4]>')]).
% 0.64/1.02 cnf('0.8.2.0',plain,
% 0.64/1.02 ( meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_8]).
% 0.64/1.02 cnf('0.9.0.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,meet(X1,join(X3,X2))) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.8.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.9.0.1',plain,
% 0.64/1.02 ( meet(X1,join(X2,X3)) = meet(X1,meet(X1,join(X3,X2))) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.9.0.0','0.7.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.9.1.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X3)) = meet(X1,meet(X1,join(X3,X2))) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.9.0.1']),
% 0.64/1.02 [weight('<103,8,2,[1,0,0,2]>')]).
% 0.64/1.02 cnf('0.9.2.0',plain,
% 0.64/1.02 ( meet(X1,meet(X1,join(X2,X3))) = meet(X1,join(X3,X2)) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_9]).
% 0.64/1.02 cnf('0.10.0.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = meet(X1,X1) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.10.1.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = meet(X1,X1) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.64/1.02 [weight('<53,9,1,[1,0,0,2]>')]).
% 0.64/1.02 cnf('0.10.2.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = meet(X1,X1) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_10]).
% 0.64/1.02 cnf('0.11.0.0',plain,
% 0.64/1.02 ( meet(X1,X1) = X1 ),
% 0.64/1.02 inference(cp,[status(thm)],['0.10.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.11.1.0',plain,
% 0.64/1.02 ( meet(X1,X1) = X1 ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.64/1.02 [weight('<19,10,1,[1,0,0,0]>')]).
% 0.64/1.02 cnf('0.11.2.0',plain,
% 0.64/1.02 ( meet(X1,X1) = X1 ),
% 0.64/1.02 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_11]).
% 0.64/1.02 cnf('0.12.0.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = meet(X1,X1) ),
% 0.64/1.02 inference(interreduction_right,[status(thm)],['0.10.2.0'])).
% 0.64/1.02 cnf('0.12.0.1',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = X1 ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.12.0.0','0.11.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.12.1.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = X1 ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.12.0.1']),
% 0.64/1.02 [weight('<41,10,11,[0,0,0,0]>')]).
% 0.64/1.02 cnf('0.12.2.0',plain,
% 0.64/1.02 ( meet(X1,join(X2,X1)) = X1 ),
% 0.64/1.02 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_12]).
% 0.64/1.02 cnf('0.13.0.0',plain,
% 0.64/1.02 ( meet(X1,join(X1,X2)) = join(meet(X2,X1),X1) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.11.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.13.0.1',plain,
% 0.64/1.02 ( X1 = join(meet(X2,X1),X1) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.13.0.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.13.1.0',plain,
% 0.64/1.02 ( X1 = join(meet(X2,X1),X1) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.13.0.1']),
% 0.64/1.02 [weight('<41,11,2,[0,0,0,4]>')]).
% 0.64/1.02 cnf('0.13.2.0',plain,
% 0.64/1.02 ( join(meet(X1,X2),X2) = X2 ),
% 0.64/1.02 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_13]).
% 0.64/1.02 cnf('0.14.0.0',plain,
% 0.64/1.02 ( X1 = join(X1,X1) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.13.2.0','0.11.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.1','L')]).
% 0.64/1.02 cnf('0.14.1.0',plain,
% 0.64/1.02 ( X1 = join(X1,X1) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.64/1.02 [weight('<19,13,11,[1,0,0,1]>')]).
% 0.64/1.02 cnf('0.14.2.0',plain,
% 0.64/1.02 ( join(X1,X1) = X1 ),
% 0.64/1.02 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_14]).
% 0.64/1.02 cnf('0.17.0.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(X2,join(X1,X1)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.14.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.17.0.1',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(X2,X1) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.17.0.0','0.14.2.0',theory(equality)]),
% 0.64/1.02 [pos('R.2','L')]).
% 0.64/1.02 cnf('0.17.1.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(X2,X1) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.17.0.1']),
% 0.64/1.02 [weight('<48,14,2,[1,0,0,0]>')]).
% 0.64/1.02 cnf('0.17.2.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(X2,X1) ),
% 0.64/1.02 inference(activate,[status(thm)],['0.17.1.0']),
% 0.64/1.02 [equation_1]).
% 0.64/1.02 cnf('0.20.0.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),X2) = meet(X1,X2) ),
% 0.64/1.02 inference(interreduction_right,[status(thm)],['0.6.2.0'])).
% 0.64/1.02 cnf('0.20.1.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),X2) = meet(X1,X2) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.64/1.02 [weight('<53,6,17,[0,0,0,0]>')]).
% 0.64/1.02 cnf('0.20.1.1',plain,
% 0.64/1.02 ( meet(X2,meet(X1,X2)) = meet(X1,X2) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.20.1.0','0.17.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.20.2.0',plain,
% 0.64/1.02 ( meet(X1,meet(X2,X1)) = meet(X2,X1) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.20.1.1',theory(equality)]),
% 0.64/1.02 [u,rule_19]).
% 0.64/1.02 cnf('0.21.0.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X1,X2)) = meet(join(X1,X2),join(X2,X1)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.20.2.0','0.9.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.21.0.1',plain,
% 0.64/1.02 ( join(meet(X2,join(X1,X2)),X1) = meet(join(X1,X2),join(X2,X1)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.21.0.0','0.4.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.21.0.2',plain,
% 0.64/1.02 ( join(X2,X1) = meet(join(X1,X2),join(X2,X1)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.21.0.1','0.12.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.1','L')]).
% 0.64/1.02 cnf('0.21.0.3',plain,
% 0.64/1.02 ( join(X2,X1) = join(X1,meet(X2,join(X1,X2))) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.21.0.2','0.3.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.21.0.4',plain,
% 0.64/1.02 ( join(X2,X1) = join(X1,X2) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.21.0.3','0.12.2.0',theory(equality)]),
% 0.64/1.02 [pos('R.2','L')]).
% 0.64/1.02 cnf('0.21.1.0',plain,
% 0.64/1.02 ( join(X2,X1) = join(X1,X2) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.21.0.4']),
% 0.64/1.02 [weight('<48,20,9,[1,0,0,0]>')]).
% 0.64/1.02 cnf('0.21.2.0',plain,
% 0.64/1.02 ( join(X1,X2) = join(X2,X1) ),
% 0.64/1.02 inference(activate,[status(thm)],['0.21.1.0']),
% 0.64/1.02 [equation_2]).
% 0.64/1.02 cnf('0.31.0.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),join(X2,X3)) = join(meet(X3,meet(X1,X2)),meet(X1,X2)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.20.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.31.0.1',plain,
% 0.64/1.02 ( meet(meet(X1,X2),join(X2,X3)) = meet(X1,X2) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.31.0.0','0.13.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.31.1.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),join(X2,X3)) = meet(X1,X2) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.31.0.1']),
% 0.64/1.02 [weight('<87,20,2,[0,0,0,4]>')]).
% 0.64/1.02 cnf('0.31.2.0',plain,
% 0.64/1.02 ( meet(meet(X1,X2),join(X2,X3)) = meet(X1,X2) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_29]).
% 0.64/1.02 cnf('0.42.0.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(join(X2,X3),meet(X1,X2)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.31.2.0','0.17.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.42.1.0',plain,
% 0.64/1.02 ( meet(X1,X2) = meet(join(X2,X3),meet(X1,X2)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.64/1.02 [weight('<87,31,17,[1,0,0,0]>')]).
% 0.64/1.02 cnf('0.42.2.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_40]).
% 0.64/1.02 cnf('0.87.0.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X2,X3)) = join(meet(X3,join(X1,X2)),X2) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.2.2.0','0.12.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.87.1.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X2,X3)) = join(meet(X3,join(X1,X2)),X2) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.87.0.0']),
% 0.64/1.02 [weight('<119,12,2,[0,0,0,4]>')]).
% 0.64/1.02 cnf('0.87.1.1',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.87.1.0','0.21.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.87.2.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.87.1.1',theory(equality)]),
% 0.64/1.02 [u,rule_84]).
% 0.64/1.02 cnf('0.88.0.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(X1,join(X2,X3))) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.17.2.0','0.3.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.88.1.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(X1,join(X2,X3))) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.88.0.0']),
% 0.64/1.02 [weight('<119,17,3,[1,0,0,0]>')]).
% 0.64/1.02 cnf('0.88.1.1',plain,
% 0.64/1.02 ( join(X2,meet(X3,join(X1,X2))) = join(X2,meet(X1,join(X2,X3))) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.88.1.0','0.87.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.88.2.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(activate,[status(thm)],['0.88.1.1']),
% 0.64/1.02 [equation_4]).
% 0.64/1.02 cnf('0.89.0.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(join(X2,X1),X3)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.88.2.0','0.17.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.89.1.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(join(X2,X1),X3)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.89.0.0']),
% 0.64/1.02 [weight('<119,88,17,[1,0,0,2]>')]).
% 0.64/1.02 cnf('0.89.2.0',plain,
% 0.64/1.02 ( join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X1,X3))) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.89.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_85]).
% 0.64/1.02 cnf('0.90.0.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X1,meet(X3,X2)))) = join(X1,meet(X3,X2)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.89.2.0','0.42.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.90.0.1',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.90.0.0','0.7.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.90.1.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.90.0.1']),
% 0.64/1.02 [weight('<103,89,42,[1,0,0,2]>')]).
% 0.64/1.02 cnf('0.90.2.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.90.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_86]).
% 0.64/1.02 cnf('0.91.0.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,join(X1,X2))) ),
% 0.64/1.02 inference(interreduction_right,[status(thm)],['0.3.2.0'])).
% 0.64/1.02 cnf('0.91.0.1',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X2,X3)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.91.0.0','0.90.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.91.1.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X2,X3)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.91.0.1']),
% 0.64/1.02 [weight('<103,3,90,[0,0,0,0]>')]).
% 0.64/1.02 cnf('0.91.2.0',plain,
% 0.64/1.02 ( meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X2,X3)) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.91.1.0',theory(equality)]),
% 0.64/1.02 [u,rule_87]).
% 0.64/1.02 cnf('0.92.0.0',plain,
% 0.64/1.02 ( join(X1,meet(X2,join(X2,X3))) = join(X1,join(X2,meet(X3,X1))) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.90.2.0','0.91.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.92.0.1',plain,
% 0.64/1.02 ( join(X1,X2) = join(X1,join(X2,meet(X3,X1))) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.92.0.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.92.1.0',plain,
% 0.64/1.02 ( join(X1,X2) = join(X1,join(X2,meet(X3,X1))) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.92.0.1']),
% 0.64/1.02 [weight('<87,91,90,[0,0,0,2]>')]).
% 0.64/1.02 cnf('0.92.2.0',plain,
% 0.64/1.02 ( join(X1,join(X2,meet(X3,X1))) = join(X1,X2) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.92.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_88]).
% 0.64/1.02 cnf('0.94.0.0',plain,
% 0.64/1.02 ( join(X1,X2) = join(X1,join(meet(X3,X1),X2)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.92.2.0','0.21.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2','L')]).
% 0.64/1.02 cnf('0.94.1.0',plain,
% 0.64/1.02 ( join(X1,X2) = join(X1,join(meet(X3,X1),X2)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.94.0.0']),
% 0.64/1.02 [weight('<87,92,21,[1,0,0,2]>')]).
% 0.64/1.02 cnf('0.94.2.0',plain,
% 0.64/1.02 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_90]).
% 0.64/1.02 cnf('0.102.0.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X1,X2),join(X3,X1)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.92.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2.2','L')]).
% 0.64/1.02 cnf('0.102.1.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X1,X2),join(X3,X1)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.102.0.0']),
% 0.64/1.02 [weight('<103,92,1,[1,0,0,4]>')]).
% 0.64/1.02 cnf('0.102.2.0',plain,
% 0.64/1.02 ( join(join(X1,X2),join(X3,X1)) = join(join(X1,X2),X3) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_98]).
% 0.64/1.02 cnf('0.107.0.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X1,X2),join(X2,X3)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.94.2.0','0.12.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.2.1','L')]).
% 0.64/1.02 cnf('0.107.1.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X1,X2),join(X2,X3)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.107.0.0']),
% 0.64/1.02 [weight('<103,94,12,[1,0,0,3]>')]).
% 0.64/1.02 cnf('0.107.2.0',plain,
% 0.64/1.02 ( join(join(X1,X2),join(X2,X3)) = join(join(X1,X2),X3) ),
% 0.64/1.02 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 0.64/1.02 [x,rule_102]).
% 0.64/1.02 cnf('0.108.0.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X3,X1),join(X1,X2)) ),
% 0.64/1.02 inference(cp,[status(thm)],['0.102.2.0','0.21.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('0.108.1.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X3,X1),join(X1,X2)) ),
% 0.64/1.02 inference(weigh,[status(thm)],['0.108.0.0']),
% 0.64/1.02 [weight('<103,102,21,[1,0,0,0]>')]).
% 0.64/1.02 cnf('0.108.1.1',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X3,X1),X2) ),
% 0.64/1.02 inference(reduction,[status(thm)],['0.108.1.0','0.107.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('0.108.2.0',plain,
% 0.64/1.02 ( join(join(X1,X2),X3) = join(join(X3,X1),X2) ),
% 0.64/1.02 inference(activate,[status(thm)],['0.108.1.1']),
% 0.64/1.02 [equation_6]).
% 0.64/1.02 cnf('1.0.0.0',conjecture,
% 0.64/1.02 ( join(join(a,b),c) = join(a,join(b,c)) ),
% 0.64/1.02 file('/tmp/WALDMEISTER_8226_n021',conjecture_1)).
% 0.64/1.02 cnf('1.0.0.1',plain,
% 0.64/1.02 ( join(join(b,a),c) = join(a,join(b,c)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['1.0.0.0','0.21.2.0',theory(equality)]),
% 0.64/1.02 [pos('L.1','L')]).
% 0.64/1.02 cnf('1.0.0.2',plain,
% 0.64/1.02 ( join(join(b,a),c) = join(a,join(c,b)) ),
% 0.64/1.02 inference(reduction,[status(thm)],['1.0.0.1','0.21.2.0',theory(equality)]),
% 0.64/1.02 [pos('R.2','L')]).
% 0.64/1.02 cnf('1.0.0.3',plain,
% 0.64/1.02 ( join(join(b,a),c) = join(join(c,b),a) ),
% 0.64/1.02 inference(reduction,[status(thm)],['1.0.0.2','0.21.2.0',theory(equality)]),
% 0.64/1.02 [pos('R','L')]).
% 0.64/1.02 cnf('1.0.0.4',plain,
% 0.64/1.02 ( join(join(c,b),a) = join(join(c,b),a) ),
% 0.64/1.02 inference(reduction,[status(thm)],['1.0.0.3','0.108.2.0',theory(equality)]),
% 0.64/1.02 [pos('L','L')]).
% 0.64/1.02 cnf('1.0.0.5',plain,
% 0.64/1.02 ( $true ),
% 0.64/1.02 inference(trivial,[status(thm)],['1.0.0.4',theory(equality)]),
% 0.64/1.02 [conjecture_1]).
% 0.64/1.02
% 0.64/1.02 Proved Goals:
% 0.64/1.02 No. 1: join(join(a,b),c) ?= join(a,join(b,c)) joined, current: join(join(c,b),a) = join(join(c,b),a)
% 0.64/1.02 1 goal was specified, which was proved.
% 0.64/1.02 % SZS output end CNFRefutation
% 0.64/1.02 #END OF PROOF
% 0.64/1.02
% 0.64/1.02 Problem WALDMEISTER_8226_n021
% 0.64/1.02 CPs.gen 8594
% 0.64/1.02 CPs.reexp 0
% 0.64/1.02 Select 738
% 0.64/1.02 R 102
% 0.64/1.02 E 6
% 0.64/1.02 vsize 6.4M
% 0.64/1.02 rss 3.8M
% 0.64/1.02 process.time 0.032s
% 0.64/1.02 wallclock.time 0.032s
% 0.64/1.02 status S
% 0.64/1.02
% 0.64/1.02
% 0.64/1.02 Waldmeister states: Goal proved.
% 0.64/1.02 % SZS status Unsatisfiable
%------------------------------------------------------------------------------