%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT149-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 07:15:23 EDT 2022
% Result : Unsatisfiable 131.01s 131.41s
% Output : CNFRefutation 131.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT149-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : woody %s
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jun 28 21:38:31 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.61/0.99 ********************************************************************************
% 0.61/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.61/0.99 * |/ | \/ | *
% 0.61/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.61/0.99 * A. Jaeger and B. Loechner | | *
% 0.61/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.61/0.99 ********************************************************************************
% 0.61/0.99
% 0.61/0.99
% 0.61/0.99 Goals:
% 0.61/0.99 ------
% 0.61/0.99
% 0.61/0.99 ( 1) meet(a,join(b,meet(c,join(b,d)))) ?=? meet(a,join(b,meet(c,join(d,meet(a,join(b,d))))))
% 0.61/0.99
% 0.61/0.99 Detected structure: Verband
% 0.61/0.99 ********************************************************************************
% 0.61/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.61/0.99 ********************************************************************************
% 0.61/0.99
% 131.01/131.41 joined goal: 1 meet(a,join(b,meet(c,join(b,d)))) ?= meet(a,join(b,meet(c,join(d,meet(a,join(b,d)))))) to meet(a,join(b,meet(c,join(d,b))))
% 131.01/131.41 goal joined
% 131.01/131.41 % SZS status Unsatisfiable
% 131.01/131.41 #START OF PROOF
% 131.01/131.41 % SZS output start CNFRefutation
% 131.01/131.41 cnf('0.1.0.0',axiom,
% 131.01/131.41 ( X1 = join(X1,X1) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.1.1.0',plain,
% 131.01/131.41 ( X1 = join(X1,X1) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.1.0.0']),
% 131.01/131.41 [weight('<0,0,0,[0,0,0,1]>')]).
% 131.01/131.41 cnf('0.1.2.0',plain,
% 131.01/131.41 ( join(X1,X1) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_1]).
% 131.01/131.41 cnf('0.2.0.0',axiom,
% 131.01/131.41 ( X1 = join(X1,meet(X1,X2)) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.2.1.0',plain,
% 131.01/131.41 ( X1 = join(X1,meet(X1,X2)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.2.0.0']),
% 131.01/131.41 [weight('<1,0,0,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.2.2.0',plain,
% 131.01/131.41 ( join(X1,meet(X1,X2)) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_2]).
% 131.01/131.41 cnf('0.3.0.0',axiom,
% 131.01/131.41 ( X1 = meet(X1,X1) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.3.1.0',plain,
% 131.01/131.41 ( X1 = meet(X1,X1) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.3.0.0']),
% 131.01/131.41 [weight('<2,0,0,[0,0,0,3]>')]).
% 131.01/131.41 cnf('0.3.2.0',plain,
% 131.01/131.41 ( meet(X1,X1) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_3]).
% 131.01/131.41 cnf('0.4.0.0',axiom,
% 131.01/131.41 ( X1 = meet(X1,join(X1,X2)) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.4.1.0',plain,
% 131.01/131.41 ( X1 = meet(X1,join(X1,X2)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.4.0.0']),
% 131.01/131.41 [weight('<3,0,0,[0,0,0,4]>')]).
% 131.01/131.41 cnf('0.4.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X1,X2)) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_4]).
% 131.01/131.41 cnf('0.5.0.0',axiom,
% 131.01/131.41 ( join(X1,X2) = join(X2,X1) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.5.1.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X2,X1) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.5.0.0']),
% 131.01/131.41 [weight('<4,0,0,[0,0,0,5]>')]).
% 131.01/131.41 cnf('0.5.2.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X2,X1) ),
% 131.01/131.41 inference(activate,[status(thm)],['0.5.1.0']),
% 131.01/131.41 [equation_1]).
% 131.01/131.41 cnf('0.6.0.0',axiom,
% 131.01/131.41 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.6.1.0',plain,
% 131.01/131.41 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.6.0.0']),
% 131.01/131.41 [weight('<5,0,0,[0,0,0,6]>')]).
% 131.01/131.41 cnf('0.6.2.0',plain,
% 131.01/131.41 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_5]).
% 131.01/131.41 cnf('0.7.0.0',axiom,
% 131.01/131.41 ( meet(X1,X2) = meet(X2,X1) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.7.1.0',plain,
% 131.01/131.41 ( meet(X1,X2) = meet(X2,X1) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.7.0.0']),
% 131.01/131.41 [weight('<6,0,0,[0,0,0,7]>')]).
% 131.01/131.41 cnf('0.7.2.0',plain,
% 131.01/131.41 ( meet(X1,X2) = meet(X2,X1) ),
% 131.01/131.41 inference(activate,[status(thm)],['0.7.1.0']),
% 131.01/131.41 [equation_2]).
% 131.01/131.41 cnf('0.8.0.0',axiom,
% 131.01/131.41 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(X2,join(X3,meet(X4,join(X1,meet(X2,X3)))))) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.8.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,join(X3,meet(X1,X4)))) = meet(X1,join(X2,join(X3,meet(X4,join(X1,meet(X2,X3)))))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.8.0.0']),
% 131.01/131.41 [weight('<7,0,0,[0,0,0,8]>')]).
% 131.01/131.41 cnf('0.8.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,join(X3,meet(X4,join(X1,meet(X2,X3)))))) = meet(X1,join(X2,join(X3,meet(X1,X4)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_6]).
% 131.01/131.41 cnf('0.9.0.0',axiom,
% 131.01/131.41 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011')).
% 131.01/131.41 cnf('0.9.1.0',plain,
% 131.01/131.41 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.9.0.0']),
% 131.01/131.41 [weight('<8,0,0,[0,0,0,9]>')]).
% 131.01/131.41 cnf('0.9.2.0',plain,
% 131.01/131.41 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_7]).
% 131.01/131.41 cnf('0.10.0.0',plain,
% 131.01/131.41 ( X1 = meet(X1,join(X2,X1)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.10.1.0',plain,
% 131.01/131.41 ( X1 = meet(X1,join(X2,X1)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.10.0.0']),
% 131.01/131.41 [weight('<5,5,4,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.10.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,X1)) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_8]).
% 131.01/131.41 cnf('0.11.0.0',plain,
% 131.01/131.41 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.6.2.0','0.1.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.1','L')]).
% 131.01/131.41 cnf('0.11.1.0',plain,
% 131.01/131.41 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.11.0.0']),
% 131.01/131.41 [weight('<5,6,1,[1,0,0,1]>')]).
% 131.01/131.41 cnf('0.11.2.0',plain,
% 131.01/131.41 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_9]).
% 131.01/131.41 cnf('0.12.0.0',plain,
% 131.01/131.41 ( X1 = join(X1,meet(X2,X1)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.2.2.0','0.7.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.12.1.0',plain,
% 131.01/131.41 ( X1 = join(X1,meet(X2,X1)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.12.0.0']),
% 131.01/131.41 [weight('<5,7,2,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.12.2.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,X1)) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_10]).
% 131.01/131.41 cnf('0.15.0.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.11.2.0','0.5.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.15.1.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.15.0.0']),
% 131.01/131.41 [weight('<5,11,5,[1,0,0,2]>')]).
% 131.01/131.41 cnf('0.15.2.0',plain,
% 131.01/131.41 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_13]).
% 131.01/131.41 cnf('0.16.0.0',plain,
% 131.01/131.41 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.1','L')]).
% 131.01/131.41 cnf('0.16.1.0',plain,
% 131.01/131.41 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.16.0.0']),
% 131.01/131.41 [weight('<7,6,2,[1,0,0,1]>')]).
% 131.01/131.41 cnf('0.16.2.0',plain,
% 131.01/131.41 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_14]).
% 131.01/131.41 cnf('0.18.0.0',plain,
% 131.01/131.41 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.10.2.0','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.18.1.0',plain,
% 131.01/131.41 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.18.0.0']),
% 131.01/131.41 [weight('<7,10,6,[1,0,0,2]>')]).
% 131.01/131.41 cnf('0.18.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,join(X3,X1))) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_16]).
% 131.01/131.41 cnf('0.19.0.0',plain,
% 131.01/131.41 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.9.2.0','0.10.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.1','L')]).
% 131.01/131.41 cnf('0.19.1.0',plain,
% 131.01/131.41 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.19.0.0']),
% 131.01/131.41 [weight('<7,10,9,[0,0,0,1]>')]).
% 131.01/131.41 cnf('0.19.2.0',plain,
% 131.01/131.41 ( meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_17]).
% 131.01/131.41 cnf('0.25.0.0',plain,
% 131.01/131.41 ( join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.6.2.0','0.15.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.1','L')]).
% 131.01/131.41 cnf('0.25.0.1',plain,
% 131.01/131.41 ( join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.25.0.0','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.25.0.2',plain,
% 131.01/131.41 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.25.0.1','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.25.1.0',plain,
% 131.01/131.41 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.25.0.2']),
% 131.01/131.41 [weight('<7,15,6,[0,0,0,1]>')]).
% 131.01/131.41 cnf('0.25.2.0',plain,
% 131.01/131.41 ( join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_23]).
% 131.01/131.41 cnf('0.29.0.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(X1,X3))) = join(X1,meet(X1,X3)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.16.2.0','0.12.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.29.0.1',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(X1,X3))) = X1 ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.29.0.0','0.2.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.29.1.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(X1,X3))) = X1 ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.29.0.1']),
% 131.01/131.41 [weight('<7,16,12,[1,0,0,2]>')]).
% 131.01/131.41 cnf('0.29.2.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(X1,X3))) = X1 ),
% 131.01/131.41 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_27]).
% 131.01/131.41 cnf('0.34.0.0',plain,
% 131.01/131.41 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 131.01/131.41 [pos('L','L')]).
% 131.01/131.41 cnf('0.34.1.0',plain,
% 131.01/131.41 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.34.0.0']),
% 131.01/131.41 [weight('<9,6,2,[1,0,0,0]>')]).
% 131.01/131.41 cnf('0.34.2.0',plain,
% 131.01/131.41 ( join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_32]).
% 131.01/131.41 cnf('0.39.0.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,join(X2,meet(X1,X3)))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X2))))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.8.2.0','0.11.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.39.0.1',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X2))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.39.0.0','0.11.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.39.0.2',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.39.0.1','0.3.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2.2.2.2','L')]).
% 131.01/131.41 cnf('0.39.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.39.0.2']),
% 131.01/131.41 [weight('<9,11,8,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.39.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_37]).
% 131.01/131.41 cnf('0.40.0.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('L','L')]).
% 131.01/131.41 cnf('0.40.1.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X1,join(X2,meet(X3,join(X1,X2)))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.40.0.0']),
% 131.01/131.41 [weight('<9,12,6,[1,0,0,0]>')]).
% 131.01/131.41 cnf('0.40.2.0',plain,
% 131.01/131.41 ( join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_38]).
% 131.01/131.41 cnf('0.76.0.0',plain,
% 131.01/131.41 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.18.2.0','0.25.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.76.1.0',plain,
% 131.01/131.41 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.76.0.0']),
% 131.01/131.41 [weight('<9,25,18,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.76.2.0',plain,
% 131.01/131.41 ( meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_74]).
% 131.01/131.41 cnf('0.183.0.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X1,join(X2,meet(X3,meet(join(X1,X2),X4)))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.29.2.0','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('L','L')]).
% 131.01/131.41 cnf('0.183.1.0',plain,
% 131.01/131.41 ( join(X1,X2) = join(X1,join(X2,meet(X3,meet(join(X1,X2),X4)))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.183.0.0']),
% 131.01/131.41 [weight('<11,29,6,[1,0,0,0]>')]).
% 131.01/131.41 cnf('0.183.2.0',plain,
% 131.01/131.41 ( join(X1,join(X2,meet(X3,meet(join(X1,X2),X4)))) = join(X1,X2) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.183.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_175]).
% 131.01/131.41 cnf('0.210.0.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X1,meet(X3,X4)))) = meet(X1,join(X2,meet(X3,meet(X4,join(X1,X2))))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.39.2.0','0.9.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2','L')]).
% 131.01/131.41 cnf('0.210.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X1,meet(X3,X4)))) = meet(X1,join(X2,meet(X3,meet(X4,join(X1,X2))))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.210.0.0']),
% 131.01/131.41 [weight('<11,39,9,[1,0,0,4]>')]).
% 131.01/131.41 cnf('0.210.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(X4,join(X1,X2))))) = meet(X1,join(X2,meet(X1,meet(X3,X4)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.210.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_202]).
% 131.01/131.41 cnf('0.214.0.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X1,meet(X2,join(X3,X1))),join(X3,X1)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.10.2.0','0.40.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.214.1.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X1,meet(X2,join(X3,X1))),join(X3,X1)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.214.0.0']),
% 131.01/131.41 [weight('<11,40,10,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.214.1.1',plain,
% 131.01/131.41 ( join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,meet(X2,join(X3,X1)))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.214.1.0','0.7.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.214.2.0',plain,
% 131.01/131.41 ( meet(join(X1,X2),join(X2,meet(X3,join(X1,X2)))) = join(X2,meet(X3,join(X1,X2))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.214.1.1',theory(equality)]),
% 131.01/131.41 [x,rule_206]).
% 131.01/131.41 cnf('0.326.0.0',plain,
% 131.01/131.41 ( join(X1,meet(join(X1,X2),X3)) = meet(join(X1,meet(join(X1,X2),X3)),join(X1,X2)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.76.2.0','0.34.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.326.1.0',plain,
% 131.01/131.41 ( join(X1,meet(join(X1,X2),X3)) = meet(join(X1,meet(join(X1,X2),X3)),join(X1,X2)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.326.0.0']),
% 131.01/131.41 [weight('<11,76,34,[1,0,0,4]>')]).
% 131.01/131.41 cnf('0.326.1.1',plain,
% 131.01/131.41 ( join(X1,meet(join(X1,X2),X3)) = meet(join(X1,X2),join(X1,meet(join(X1,X2),X3))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.326.1.0','0.7.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.326.2.0',plain,
% 131.01/131.41 ( meet(join(X1,X2),join(X1,meet(join(X1,X2),X3))) = join(X1,meet(join(X1,X2),X3)) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.326.1.1',theory(equality)]),
% 131.01/131.41 [x,rule_318]).
% 131.01/131.41 cnf('0.2019.0.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(join(X3,X1),X4))) = meet(join(X1,meet(X2,meet(join(X3,X1),X4))),join(X3,X1)) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.10.2.0','0.183.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.2019.1.0',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(join(X3,X1),X4))) = meet(join(X1,meet(X2,meet(join(X3,X1),X4))),join(X3,X1)) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.2019.0.0']),
% 131.01/131.41 [weight('<13,183,10,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.2019.1.1',plain,
% 131.01/131.41 ( join(X1,meet(X2,meet(join(X3,X1),X4))) = meet(join(X3,X1),join(X1,meet(X2,meet(join(X3,X1),X4)))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.2019.1.0','0.7.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.2019.2.0',plain,
% 131.01/131.41 ( meet(join(X1,X2),join(X2,meet(X3,meet(join(X1,X2),X4)))) = join(X2,meet(X3,meet(join(X1,X2),X4))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.2019.1.1',theory(equality)]),
% 131.01/131.41 [x,rule_2011]).
% 131.01/131.41 cnf('0.2191.0.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(X4,join(join(X5,X1),X2))))) = meet(X1,meet(join(X5,X1),join(X2,meet(join(X5,X1),meet(X3,X4))))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.19.2.0','0.210.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.2191.0.1',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(X4,join(X5,join(X1,X2)))))) = meet(X1,meet(join(X5,X1),join(X2,meet(join(X5,X1),meet(X3,X4))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.2191.0.0','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2.2.2','L')]).
% 131.01/131.41 cnf('0.2191.0.2',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(X4,join(X5,join(X1,X2)))))) = meet(X1,join(X2,meet(join(X5,X1),meet(X3,X4)))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.2191.0.1','0.19.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.2191.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(X4,join(X5,join(X1,X2)))))) = meet(X1,join(X2,meet(join(X5,X1),meet(X3,X4)))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.2191.0.2']),
% 131.01/131.41 [weight('<13,210,19,[0,0,0,2]>')]).
% 131.01/131.41 cnf('0.2191.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(X4,join(X5,join(X1,X2)))))) = meet(X1,join(X2,meet(join(X5,X1),meet(X3,X4)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.2191.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_2183]).
% 131.01/131.41 cnf('0.4449.0.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(join(X3,X1),meet(X4,join(X3,X2))))) = meet(X1,join(X2,meet(X4,join(X3,X2)))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.2191.2.0','0.76.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2.2','L')]).
% 131.01/131.41 cnf('0.4449.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(join(X3,X1),meet(X4,join(X3,X2))))) = meet(X1,join(X2,meet(X4,join(X3,X2)))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.4449.0.0']),
% 131.01/131.41 [weight('<13,2191,76,[1,0,0,6]>')]).
% 131.01/131.41 cnf('0.4449.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(join(X3,X1),meet(X4,join(X3,X2))))) = meet(X1,join(X2,meet(X4,join(X3,X2)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.4449.1.0',theory(equality)]),
% 131.01/131.41 [u,rule_4421]).
% 131.01/131.41 cnf('0.4642.0.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,X2)))) = meet(X1,join(X2,meet(meet(X3,join(X4,X2)),join(X4,X1)))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.4449.2.0','0.7.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2','L')]).
% 131.01/131.41 cnf('0.4642.0.1',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,X2)))) = meet(X1,join(X2,meet(X3,meet(join(X4,X2),join(X4,X1))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4642.0.0','0.9.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2.2','L')]).
% 131.01/131.41 cnf('0.4642.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,X2)))) = meet(X1,join(X2,meet(X3,meet(join(X4,X2),join(X4,X1))))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.4642.0.1']),
% 131.01/131.41 [weight('<13,4449,7,[1,0,0,4]>')]).
% 131.01/131.41 cnf('0.4642.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,meet(join(X4,X2),join(X4,X1))))) = meet(X1,join(X2,meet(X3,join(X4,X2)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.4642.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_4596]).
% 131.01/131.41 cnf('0.4682.0.0',plain,
% 131.01/131.41 ( meet(meet(X1,join(join(X2,X3),X2)),join(X3,meet(X4,join(X2,X3)))) = meet(meet(X1,join(join(X2,X3),X2)),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1)))))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.4642.2.0','0.39.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2.2','L')]).
% 131.01/131.41 cnf('0.4682.0.1',plain,
% 131.01/131.41 ( meet(X1,meet(join(join(X2,X3),X2),join(X3,meet(X4,join(X2,X3))))) = meet(meet(X1,join(join(X2,X3),X2)),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.0','0.9.2.0',theory(equality)]),
% 131.01/131.41 [pos('L','L')]).
% 131.01/131.41 cnf('0.4682.0.2',plain,
% 131.01/131.41 ( meet(X1,meet(join(X2,join(X3,X2)),join(X3,meet(X4,join(X2,X3))))) = meet(meet(X1,join(join(X2,X3),X2)),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.1','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.1','L')]).
% 131.01/131.41 cnf('0.4682.0.3',plain,
% 131.01/131.41 ( meet(X1,meet(join(X2,X3),join(X3,meet(X4,join(X2,X3))))) = meet(meet(X1,join(join(X2,X3),X2)),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.2','0.15.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.1','L')]).
% 131.01/131.41 cnf('0.4682.0.4',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(meet(X1,join(join(X2,X3),X2)),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.3','0.214.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2','L')]).
% 131.01/131.41 cnf('0.4682.0.5',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(X1,meet(join(join(X2,X3),X2),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1))))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.4','0.9.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('0.4682.0.6',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(X1,meet(join(X2,join(X3,X2)),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1))))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.5','0.6.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2.1','L')]).
% 131.01/131.41 cnf('0.4682.0.7',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(X1,meet(join(X2,X3),join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1))))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.6','0.15.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2.1','L')]).
% 131.01/131.41 cnf('0.4682.0.8',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(X1,join(X3,meet(X4,meet(join(X2,X3),join(X2,meet(join(X2,X3),X1)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.7','0.2019.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2','L')]).
% 131.01/131.41 cnf('0.4682.0.9',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(X1,join(X3,meet(X4,join(X2,meet(join(X2,X3),X1))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['0.4682.0.8','0.326.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2.2.2','L')]).
% 131.01/131.41 cnf('0.4682.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X3,meet(X4,join(X2,X3)))) = meet(X1,join(X3,meet(X4,join(X2,meet(join(X2,X3),X1))))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.4682.0.9']),
% 131.01/131.41 [weight('<13,4642,39,[1,0,0,6]>')]).
% 131.01/131.41 cnf('0.4682.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,meet(join(X4,X2),X1))))) = meet(X1,join(X2,meet(X3,join(X4,X2)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.4682.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_4621]).
% 131.01/131.41 cnf('0.4691.0.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,X2)))) = meet(X1,join(X2,meet(X3,join(X4,meet(X1,join(X4,X2)))))) ),
% 131.01/131.41 inference(cp,[status(thm)],['0.4682.2.0','0.7.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2.2.2','L')]).
% 131.01/131.41 cnf('0.4691.1.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,X2)))) = meet(X1,join(X2,meet(X3,join(X4,meet(X1,join(X4,X2)))))) ),
% 131.01/131.41 inference(weigh,[status(thm)],['0.4691.0.0']),
% 131.01/131.41 [weight('<13,4682,7,[1,0,0,8]>')]).
% 131.01/131.41 cnf('0.4691.2.0',plain,
% 131.01/131.41 ( meet(X1,join(X2,meet(X3,join(X4,meet(X1,join(X4,X2)))))) = meet(X1,join(X2,meet(X3,join(X4,X2)))) ),
% 131.01/131.41 inference(orient,[status(thm)],['0.4691.1.0',theory(equality)]),
% 131.01/131.41 [x,rule_4627]).
% 131.01/131.41 cnf('1.0.0.0',conjecture,
% 131.01/131.41 ( meet(a,join(b,meet(c,join(b,d)))) = meet(a,join(b,meet(c,join(d,meet(a,join(b,d)))))) ),
% 131.01/131.41 file('/tmp/WALDMEISTER_11102_n011',conjecture_1)).
% 131.01/131.41 cnf('1.0.0.1',plain,
% 131.01/131.41 ( meet(a,join(b,meet(c,join(d,b)))) = meet(a,join(b,meet(c,join(d,meet(a,join(b,d)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['1.0.0.0','0.5.2.0',theory(equality)]),
% 131.01/131.41 [pos('L.2.2.2','L')]).
% 131.01/131.41 cnf('1.0.0.2',plain,
% 131.01/131.41 ( meet(a,join(b,meet(c,join(d,b)))) = meet(a,join(b,meet(c,join(d,meet(a,join(d,b)))))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['1.0.0.1','0.5.2.0',theory(equality)]),
% 131.01/131.41 [pos('R.2.2.2.2.2','L')]).
% 131.01/131.41 cnf('1.0.0.3',plain,
% 131.01/131.41 ( meet(a,join(b,meet(c,join(d,b)))) = meet(a,join(b,meet(c,join(d,b)))) ),
% 131.01/131.41 inference(reduction,[status(thm)],['1.0.0.2','0.4691.2.0',theory(equality)]),
% 131.01/131.41 [pos('R','L')]).
% 131.01/131.41 cnf('1.0.0.4',plain,
% 131.01/131.41 ( $true ),
% 131.01/131.41 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 131.01/131.41 [conjecture_1]).
% 131.01/131.41
% 131.01/131.41 Proved Goals:
% 131.01/131.41 No. 1: meet(a,join(b,meet(c,join(b,d)))) ?= meet(a,join(b,meet(c,join(d,meet(a,join(b,d)))))) joined, current: meet(a,join(b,meet(c,join(d,b)))) = meet(a,join(b,meet(c,join(d,b))))
% 131.01/131.41 1 goal was specified, which was proved.
% 131.01/131.41 % SZS output end CNFRefutation
% 131.01/131.41 #END OF PROOF
% 131.01/131.41
% 131.01/131.41 Problem WALDMEISTER_11102_n011
% 131.01/131.41 CPs.gen 28286915
% 131.01/131.41 CPs.reexp 0
% 131.01/131.41 Select 498140
% 131.01/131.41 R 4627
% 131.01/131.41 E 64
% 131.01/131.41 vsize 12.8M
% 131.01/131.41 rss 8.0M
% 131.01/131.41 process.time 130.426s
% 131.01/131.41 wallclock.time 130.427s
% 131.01/131.41 status S
% 131.01/131.41
% 131.01/131.41
% 131.01/131.41 Waldmeister states: Goal proved.
% 131.01/131.41 % SZS status Unsatisfiable
%------------------------------------------------------------------------------