TSTP Solution File: LCL109-10 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL109-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n006.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 16:03:33 EDT 2022
% Result : Unsatisfiable 0.31s 0.76s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : LCL109-10 : TPTP v8.1.0. Released v7.5.0.
% 0.00/0.07 % Command : woody %s
% 0.06/0.25 % Computer : n006.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Sun Jul 3 08:58:07 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.31/0.71 ********************************************************************************
% 0.31/0.71 * W A L D M E I S T E R \| \ / \|/ *
% 0.31/0.71 * |/ | \/ | *
% 0.31/0.71 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.31/0.71 * A. Jaeger and B. Loechner | | *
% 0.31/0.71 * <waldmeister@informatik.uni-kl.de> | *
% 0.31/0.71 ********************************************************************************
% 0.31/0.71
% 0.31/0.71
% 0.31/0.71 Goals:
% 0.31/0.71 ------
% 0.31/0.71
% 0.31/0.71 ( 1) implies(implies(implies(a,b),implies(b,a)),implies(b,a)) ?=? truth
% 0.31/0.71
% 0.31/0.71 Detected structure: WajsbergAlgebra
% 0.31/0.71 ********************************************************************************
% 0.31/0.71 ****************************** COMPLETION - PROOF ******************************
% 0.31/0.71 ********************************************************************************
% 0.31/0.71
% 0.31/0.76 joined goal: 1 implies(implies(implies(a,b),implies(b,a)),implies(b,a)) ?= truth to truth
% 0.31/0.76 goal joined
% 0.31/0.76 % SZS status Unsatisfiable
% 0.31/0.76 #START OF PROOF
% 0.31/0.76 % SZS output start CNFRefutation
% 0.31/0.76 cnf('0.1.0.0',axiom,
% 0.31/0.76 ( X1 = implies(truth,X1) ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.1.1.0',plain,
% 0.31/0.76 ( X1 = implies(truth,X1) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.31/0.76 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.31/0.76 cnf('0.1.2.0',plain,
% 0.31/0.76 ( implies(truth,X1) = X1 ),
% 0.31/0.76 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_1]).
% 0.31/0.76 cnf('0.2.0.0',axiom,
% 0.31/0.76 ( X1 = not(not(X1)) ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.2.1.0',plain,
% 0.31/0.76 ( X1 = not(not(X1)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.31/0.76 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.31/0.76 cnf('0.2.2.0',plain,
% 0.31/0.76 ( not(not(X1)) = X1 ),
% 0.31/0.76 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_2]).
% 0.31/0.76 cnf('0.5.0.0',axiom,
% 0.31/0.76 ( implies(X1,X2) = implies(not(X2),not(X1)) ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.5.1.0',plain,
% 0.31/0.76 ( implies(X1,X2) = implies(not(X2),not(X1)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.31/0.76 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.31/0.76 cnf('0.5.2.0',plain,
% 0.31/0.76 ( implies(not(X1),not(X2)) = implies(X2,X1) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_5]).
% 0.31/0.76 cnf('0.7.0.0',axiom,
% 0.31/0.76 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.7.1.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.31/0.76 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.31/0.76 cnf('0.7.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 inference(activate,[status(thm)],['0.7.1.0']),
% 0.31/0.76 [equation_1]).
% 0.31/0.76 cnf('0.8.0.0',axiom,
% 0.31/0.76 ( implies(X1,implies(X2,X1)) = truth ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.8.1.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,X1)) = truth ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.31/0.76 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.31/0.76 cnf('0.8.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,X1)) = truth ),
% 0.31/0.76 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.31/0.76 [u,rule_7]).
% 0.31/0.76 cnf('0.11.0.0',axiom,
% 0.31/0.76 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.11.1.0',plain,
% 0.31/0.76 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.31/0.76 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.31/0.76 cnf('0.11.2.0',plain,
% 0.31/0.76 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.31/0.76 inference(activate,[status(thm)],['0.11.1.0']),
% 0.31/0.76 [equation_2]).
% 0.31/0.76 cnf('0.14.0.0',axiom,
% 0.31/0.76 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006')).
% 0.31/0.76 cnf('0.14.1.0',plain,
% 0.31/0.76 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.31/0.76 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.31/0.76 cnf('0.14.1.1',plain,
% 0.31/0.76 ( implies(X2,implies(implies(not(X1),not(X2)),X1)) = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.14.1.0','0.7.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('0.14.1.2',plain,
% 0.31/0.76 ( implies(X2,implies(implies(X2,X1),X1)) = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.14.1.1','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2.1','L')]).
% 0.31/0.76 cnf('0.14.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(implies(X1,X2),X2)) = truth ),
% 0.31/0.76 inference(orient,[status(thm)],['0.14.1.2',theory(equality)]),
% 0.31/0.76 [u,rule_12]).
% 0.31/0.76 cnf('0.18.0.0',plain,
% 0.31/0.76 ( truth = implies(not(X1),implies(X1,X2)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.8.2.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2','L')]).
% 0.31/0.76 cnf('0.18.1.0',plain,
% 0.31/0.76 ( truth = implies(not(X1),implies(X1,X2)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.31/0.76 [weight('<55,8,5,[1,0,0,2]>')]).
% 0.31/0.76 cnf('0.18.1.1',plain,
% 0.31/0.76 ( truth = implies(X1,implies(not(X1),X2)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.18.1.0','0.7.2.0',theory(equality)]),
% 0.31/0.76 [pos('R','L')]).
% 0.31/0.76 cnf('0.18.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(not(X1),X2)) = truth ),
% 0.31/0.76 inference(orient,[status(thm)],['0.18.1.1',theory(equality)]),
% 0.31/0.76 [x,rule_16]).
% 0.31/0.76 cnf('0.35.0.0',plain,
% 0.31/0.76 ( implies(X1,not(X2)) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.35.1.0',plain,
% 0.31/0.76 ( implies(X1,not(X2)) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.31/0.76 [weight('<80,5,2,[1,0,0,1]>')]).
% 0.31/0.76 cnf('0.35.2.0',plain,
% 0.31/0.76 ( implies(X1,not(X2)) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(activate,[status(thm)],['0.35.1.0']),
% 0.31/0.76 [equation_3]).
% 0.31/0.76 cnf('0.36.0.0',plain,
% 0.31/0.76 ( implies(not(X1),X2) = implies(not(X2),X1) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2','L')]).
% 0.31/0.76 cnf('0.36.1.0',plain,
% 0.31/0.76 ( implies(not(X1),X2) = implies(not(X2),X1) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.36.0.0']),
% 0.31/0.76 [weight('<80,5,2,[1,0,0,3]>')]).
% 0.31/0.76 cnf('0.36.2.0',plain,
% 0.31/0.76 ( implies(not(X1),X2) = implies(not(X2),X1) ),
% 0.31/0.76 inference(activate,[status(thm)],['0.36.1.0']),
% 0.31/0.76 [equation_4]).
% 0.31/0.76 cnf('0.38.0.0',plain,
% 0.31/0.76 ( implies(implies(implies(X1,X2),X2),X2) = implies(truth,implies(X1,X2)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.11.2.0','0.8.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.38.0.1',plain,
% 0.31/0.76 ( implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 0.31/0.76 [pos('R','L')]).
% 0.31/0.76 cnf('0.38.1.0',plain,
% 0.31/0.76 ( implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.38.0.1']),
% 0.31/0.76 [weight('<87,11,8,[1,0,0,1]>')]).
% 0.31/0.76 cnf('0.38.2.0',plain,
% 0.31/0.76 ( implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.31/0.76 [u,rule_34]).
% 0.31/0.76 cnf('0.39.0.0',plain,
% 0.31/0.76 ( implies(X1,X2) = implies(implies(implies(X2,X1),X1),X2) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.38.2.0','0.11.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.39.1.0',plain,
% 0.31/0.76 ( implies(X1,X2) = implies(implies(implies(X2,X1),X1),X2) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.31/0.76 [weight('<87,38,11,[1,0,0,1]>')]).
% 0.31/0.76 cnf('0.39.2.0',plain,
% 0.31/0.76 ( implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_35]).
% 0.31/0.76 cnf('0.47.0.0',plain,
% 0.31/0.76 ( implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.36.2.0','0.7.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('0.47.1.0',plain,
% 0.31/0.76 ( implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.31/0.76 [weight('<90,36,7,[1,0,0,0]>')]).
% 0.31/0.76 cnf('0.47.2.0',plain,
% 0.31/0.76 ( implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.31/0.76 [u,rule_43]).
% 0.31/0.76 cnf('0.48.0.0',plain,
% 0.31/0.76 ( implies(not(X1),implies(X2,not(X3))) = implies(X2,implies(X3,X1)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.7.2.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2','L')]).
% 0.31/0.76 cnf('0.48.1.0',plain,
% 0.31/0.76 ( implies(not(X1),implies(X2,not(X3))) = implies(X2,implies(X3,X1)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.48.0.0']),
% 0.31/0.76 [weight('<103,7,5,[1,0,0,2]>')]).
% 0.31/0.76 cnf('0.48.2.0',plain,
% 0.31/0.76 ( implies(not(X1),implies(X2,not(X3))) = implies(X2,implies(X3,X1)) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 0.31/0.76 [u,rule_44]).
% 0.31/0.76 cnf('0.76.0.0',plain,
% 0.31/0.76 ( implies(not(X1),not(X2)) = implies(implies(implies(X2,X1),not(X2)),not(X2)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.38.2.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1.1','L')]).
% 0.31/0.76 cnf('0.76.0.1',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(implies(implies(X2,X1),not(X2)),not(X2)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.76.0.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('0.76.1.0',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(implies(implies(X2,X1),not(X2)),not(X2)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.76.0.1']),
% 0.31/0.76 [weight('<129,38,5,[1,0,0,2]>')]).
% 0.31/0.76 cnf('0.76.1.1',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(X2,not(implies(implies(X2,X1),not(X2)))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.76.1.0','0.35.2.0',theory(equality)]),
% 0.31/0.76 [pos('R','L')]).
% 0.31/0.76 cnf('0.76.1.2',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(X2,not(implies(X2,not(implies(X2,X1))))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.76.1.1','0.35.2.0',theory(equality)]),
% 0.31/0.76 [pos('R.2.1','L')]).
% 0.31/0.76 cnf('0.76.2.0',plain,
% 0.31/0.76 ( implies(X1,not(implies(X1,not(implies(X1,X2))))) = implies(X1,X2) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.76.1.2',theory(equality)]),
% 0.31/0.76 [x,rule_72]).
% 0.31/0.76 cnf('0.170.0.0',plain,
% 0.31/0.76 ( implies(implies(not(implies(X1,not(implies(X1,X2)))),X1),X1) = implies(implies(X1,X2),not(implies(X1,not(implies(X1,X2))))) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.11.2.0','0.76.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.170.0.1',plain,
% 0.31/0.76 ( implies(implies(X1,implies(not(X1),not(implies(X1,X2)))),X1) = implies(implies(X1,X2),not(implies(X1,not(implies(X1,X2))))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.170.0.0','0.47.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.170.0.2',plain,
% 0.31/0.76 ( implies(truth,X1) = implies(implies(X1,X2),not(implies(X1,not(implies(X1,X2))))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.170.0.1','0.18.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.170.0.3',plain,
% 0.31/0.76 ( X1 = implies(implies(X1,X2),not(implies(X1,not(implies(X1,X2))))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.170.0.2','0.1.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('0.170.1.0',plain,
% 0.31/0.76 ( X1 = implies(implies(X1,X2),not(implies(X1,not(implies(X1,X2))))) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.170.0.3']),
% 0.31/0.76 [weight('<155,76,11,[0,0,0,1]>')]).
% 0.31/0.76 cnf('0.170.2.0',plain,
% 0.31/0.76 ( implies(implies(X1,X2),not(implies(X1,not(implies(X1,X2))))) = X1 ),
% 0.31/0.76 inference(orient,[status(thm)],['0.170.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_166]).
% 0.31/0.76 cnf('0.175.0.0',plain,
% 0.31/0.76 ( not(X1) = implies(implies(X2,X1),not(implies(not(X1),not(implies(not(X1),not(X2)))))) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.170.2.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.175.0.1',plain,
% 0.31/0.76 ( not(X1) = implies(implies(X2,X1),not(implies(implies(not(X1),not(X2)),X1))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.175.0.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('R.2.1','L')]).
% 0.31/0.76 cnf('0.175.0.2',plain,
% 0.31/0.76 ( not(X1) = implies(implies(X2,X1),not(implies(implies(X2,X1),X1))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.175.0.1','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('R.2.1.1','L')]).
% 0.31/0.76 cnf('0.175.1.0',plain,
% 0.31/0.76 ( not(X1) = implies(implies(X2,X1),not(implies(implies(X2,X1),X1))) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.175.0.2']),
% 0.31/0.76 [weight('<142,170,5,[1,0,0,1]>')]).
% 0.31/0.76 cnf('0.175.2.0',plain,
% 0.31/0.76 ( implies(implies(X1,X2),not(implies(implies(X1,X2),X2))) = not(X2) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.175.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_171]).
% 0.31/0.76 cnf('0.176.0.0',plain,
% 0.31/0.76 ( not(X1) = implies(implies(implies(X1,X2),X2),not(implies(implies(implies(X2,X1),X1),X1))) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.175.2.0','0.11.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('0.176.0.1',plain,
% 0.31/0.76 ( not(X1) = implies(implies(implies(X1,X2),X2),not(implies(X2,X1))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.176.0.0','0.38.2.0',theory(equality)]),
% 0.31/0.76 [pos('R.2.1','L')]).
% 0.31/0.76 cnf('0.176.1.0',plain,
% 0.31/0.76 ( not(X1) = implies(implies(implies(X1,X2),X2),not(implies(X2,X1))) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.176.0.1']),
% 0.31/0.76 [weight('<142,175,11,[1,0,0,1]>')]).
% 0.31/0.76 cnf('0.176.1.1',plain,
% 0.31/0.76 ( not(X1) = implies(implies(X2,X1),not(implies(implies(X1,X2),X2))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.176.1.0','0.35.2.0',theory(equality)]),
% 0.31/0.76 [pos('R','L')]).
% 0.31/0.76 cnf('0.176.2.0',plain,
% 0.31/0.76 ( implies(implies(X1,X2),not(implies(implies(X2,X1),X1))) = not(X2) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.176.1.1',theory(equality)]),
% 0.31/0.76 [x,rule_172]).
% 0.31/0.76 cnf('0.207.0.0',plain,
% 0.31/0.76 ( implies(implies(implies(not(X1),X2),X2),implies(X1,X3)) = implies(not(X3),implies(X2,not(X1))) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.48.2.0','0.39.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2','L')]).
% 0.31/0.76 cnf('0.207.0.1',plain,
% 0.31/0.76 ( implies(implies(implies(not(X1),X2),X2),implies(X1,X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.207.0.0','0.48.2.0',theory(equality)]),
% 0.31/0.76 [pos('R','L')]).
% 0.31/0.76 cnf('0.207.1.0',plain,
% 0.31/0.76 ( implies(implies(implies(not(X1),X2),X2),implies(X1,X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.207.0.1']),
% 0.31/0.76 [weight('<175,48,39,[1,0,0,3]>')]).
% 0.31/0.76 cnf('0.207.1.1',plain,
% 0.31/0.76 ( implies(X1,implies(implies(implies(not(X1),X2),X2),X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.207.1.0','0.7.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('0.207.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(implies(implies(not(X1),X2),X2),X3)) = implies(X2,implies(X1,X3)) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.207.1.1',theory(equality)]),
% 0.31/0.76 [u,rule_196]).
% 0.31/0.76 cnf('0.208.0.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,not(implies(implies(X1,implies(not(X2),X1)),implies(not(X2),X1))))) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.207.2.0','0.176.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2','L')]).
% 0.31/0.76 cnf('0.208.0.1',plain,
% 0.31/0.76 ( implies(X1,implies(X2,not(implies(truth,implies(not(X2),X1))))) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.208.0.0','0.8.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2.2.1.1','L')]).
% 0.31/0.76 cnf('0.208.0.2',plain,
% 0.31/0.76 ( implies(X1,implies(X2,not(implies(not(X2),X1)))) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.208.0.1','0.1.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2.2.1','L')]).
% 0.31/0.76 cnf('0.208.1.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,not(implies(not(X2),X1)))) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.208.0.2']),
% 0.31/0.76 [weight('<139,207,176,[1,0,0,2]>')]).
% 0.31/0.76 cnf('0.208.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(X2,not(implies(not(X2),X1)))) = implies(X2,not(X1)) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.208.1.0',theory(equality)]),
% 0.31/0.76 [u,rule_197]).
% 0.31/0.76 cnf('0.209.0.0',plain,
% 0.31/0.76 ( implies(not(X1),not(X2)) = implies(X2,implies(not(X1),not(implies(X1,X2)))) ),
% 0.31/0.76 inference(cp,[status(thm)],['0.208.2.0','0.2.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2.2.1.1','L')]).
% 0.31/0.76 cnf('0.209.0.1',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(X2,implies(not(X1),not(implies(X1,X2)))) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.209.0.0','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('0.209.0.2',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(X2,implies(implies(X1,X2),X1)) ),
% 0.31/0.76 inference(reduction,[status(thm)],['0.209.0.1','0.5.2.0',theory(equality)]),
% 0.31/0.76 [pos('R.2','L')]).
% 0.31/0.76 cnf('0.209.1.0',plain,
% 0.31/0.76 ( implies(X2,X1) = implies(X2,implies(implies(X1,X2),X1)) ),
% 0.31/0.76 inference(weigh,[status(thm)],['0.209.0.2']),
% 0.31/0.76 [weight('<87,208,2,[1,0,0,6]>')]).
% 0.31/0.76 cnf('0.209.2.0',plain,
% 0.31/0.76 ( implies(X1,implies(implies(X2,X1),X2)) = implies(X1,X2) ),
% 0.31/0.76 inference(orient,[status(thm)],['0.209.1.0',theory(equality)]),
% 0.31/0.76 [x,rule_198]).
% 0.31/0.76 cnf('1.0.0.0',conjecture,
% 0.31/0.76 ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth ),
% 0.31/0.76 file('/tmp/WALDMEISTER_7511_n006',conjecture_1)).
% 0.31/0.76 cnf('1.0.0.1',plain,
% 0.31/0.76 ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['1.0.0.0','0.11.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('1.0.0.2',plain,
% 0.31/0.76 ( implies(implies(a,implies(implies(b,a),b)),implies(a,b)) = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['1.0.0.1','0.7.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.1','L')]).
% 0.31/0.76 cnf('1.0.0.3',plain,
% 0.31/0.76 ( implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['1.0.0.2','0.7.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('1.0.0.4',plain,
% 0.31/0.76 ( implies(a,implies(implies(a,b),b)) = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['1.0.0.3','0.209.2.0',theory(equality)]),
% 0.31/0.76 [pos('L.2.1','L')]).
% 0.31/0.76 cnf('1.0.0.5',plain,
% 0.31/0.76 ( truth = truth ),
% 0.31/0.76 inference(reduction,[status(thm)],['1.0.0.4','0.14.2.0',theory(equality)]),
% 0.31/0.76 [pos('L','L')]).
% 0.31/0.76 cnf('1.0.0.6',plain,
% 0.31/0.76 ( $true ),
% 0.31/0.76 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 0.31/0.76 [conjecture_1]).
% 0.31/0.76
% 0.31/0.76 Proved Goals:
% 0.31/0.76 No. 1: implies(implies(implies(a,b),implies(b,a)),implies(b,a)) ?= truth joined, current: truth = truth
% 0.31/0.76 1 goal was specified, which was proved.
% 0.31/0.76 % SZS output end CNFRefutation
% 0.31/0.76 #END OF PROOF
% 0.31/0.76
% 0.31/0.76 Problem WALDMEISTER_7511_n006
% 0.31/0.76 CPs.gen 31345
% 0.31/0.76 CPs.reexp 0
% 0.31/0.76 Select 1311
% 0.31/0.76 R 198
% 0.31/0.76 E 11
% 0.31/0.76 vsize 6.5M
% 0.31/0.76 rss 4.0M
% 0.31/0.76 process.time 0.051s
% 0.31/0.76 wallclock.time 0.051s
% 0.31/0.76 status S
% 0.31/0.76
% 0.31/0.76
% 0.31/0.76 Waldmeister states: Goal proved.
% 0.31/0.76 % SZS status Unsatisfiable
%------------------------------------------------------------------------------