TSTP Solution File: LCL156-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n008.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 16:03:54 EDT 2022
% Result : Unsatisfiable 0.55s 1.00s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n008.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 : Sun Jul 3 11:35:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.96 ********************************************************************************
% 0.55/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.55/0.96 * |/ | \/ | *
% 0.55/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.55/0.96 * A. Jaeger and B. Loechner | | *
% 0.55/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.55/0.96 ********************************************************************************
% 0.55/0.96
% 0.55/0.96
% 0.55/0.96 Goals:
% 0.55/0.96 ------
% 0.55/0.96
% 0.55/0.96 ( 1) and_star(x,truth) ?=? x
% 0.55/0.96
% 0.55/0.96 Detected structure: WajsbergAlgebra
% 0.55/0.96 ********************************************************************************
% 0.55/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.55/0.96 ********************************************************************************
% 0.55/0.96
% 0.55/1.00 joined goal: 1 and_star(x,truth) ?= x to x
% 0.55/1.00 goal joined
% 0.55/1.00 % SZS status Unsatisfiable
% 0.55/1.00 #START OF PROOF
% 0.55/1.00 % SZS output start CNFRefutation
% 0.55/1.00 cnf('0.1.0.0',axiom,
% 0.55/1.00 ( X1 = implies(truth,X1) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.1.1.0',plain,
% 0.55/1.00 ( X1 = implies(truth,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.55/1.00 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.55/1.00 cnf('0.1.2.0',plain,
% 0.55/1.00 ( implies(truth,X1) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_1]).
% 0.55/1.00 cnf('0.2.0.0',axiom,
% 0.55/1.00 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.2.1.0',plain,
% 0.55/1.00 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.55/1.00 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.55/1.00 cnf('0.2.2.0',plain,
% 0.55/1.00 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.55/1.00 inference(activate,[status(thm)],['0.2.1.0']),
% 0.55/1.00 [equation_1]).
% 0.55/1.00 cnf('0.3.0.0',axiom,
% 0.55/1.00 ( implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.3.1.0',plain,
% 0.55/1.00 ( implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.55/1.00 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.55/1.00 cnf('0.3.2.0',plain,
% 0.55/1.00 ( implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_2]).
% 0.55/1.00 cnf('0.4.0.0',axiom,
% 0.55/1.00 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.4.1.0',plain,
% 0.55/1.00 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.55/1.00 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.55/1.00 cnf('0.4.2.0',plain,
% 0.55/1.00 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_3]).
% 0.55/1.00 cnf('0.5.0.0',axiom,
% 0.55/1.00 ( implies(not(X1),X2) = or(X1,X2) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.5.1.0',plain,
% 0.55/1.00 ( implies(not(X1),X2) = or(X1,X2) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.55/1.00 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.55/1.00 cnf('0.5.2.0',plain,
% 0.55/1.00 ( implies(not(X1),X2) = or(X1,X2) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_4]).
% 0.55/1.00 cnf('0.6.0.0',axiom,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and(X1,X2) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.6.1.0',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and(X1,X2) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.55/1.00 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.55/1.00 cnf('0.6.2.0',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and(X1,X2) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_5]).
% 0.55/1.00 cnf('0.7.0.0',axiom,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and_star(X1,X2) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.7.1.0',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and_star(X1,X2) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.55/1.00 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.55/1.00 cnf('0.7.1.1',plain,
% 0.55/1.00 ( and(X1,X2) = and_star(X1,X2) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.7.1.0','0.6.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.7.2.0',plain,
% 0.55/1.00 ( and(X1,X2) = and_star(X1,X2) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.7.1.1',theory(equality)]),
% 0.55/1.00 [u,rule_6]).
% 0.55/1.00 cnf('0.8.0.0',axiom,
% 0.55/1.00 ( not(truth) = falsehood ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.8.1.0',plain,
% 0.55/1.00 ( not(truth) = falsehood ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.55/1.00 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.55/1.00 cnf('0.8.2.0',plain,
% 0.55/1.00 ( not(truth) = falsehood ),
% 0.55/1.00 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_7]).
% 0.55/1.00 cnf('0.9.0.0',axiom,
% 0.55/1.00 ( or(X1,X2) = or(X2,X1) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.9.1.0',plain,
% 0.55/1.00 ( or(X1,X2) = or(X2,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.55/1.00 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.55/1.00 cnf('0.9.2.0',plain,
% 0.55/1.00 ( or(X1,X2) = or(X2,X1) ),
% 0.55/1.00 inference(activate,[status(thm)],['0.9.1.0']),
% 0.55/1.00 [equation_2]).
% 0.55/1.00 cnf('0.10.0.0',axiom,
% 0.55/1.00 ( or(X1,or(X2,X3)) = or(or(X1,X2),X3) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.10.1.0',plain,
% 0.55/1.00 ( or(X1,or(X2,X3)) = or(or(X1,X2),X3) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.55/1.00 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.55/1.00 cnf('0.10.2.0',plain,
% 0.55/1.00 ( or(or(X1,X2),X3) = or(X1,or(X2,X3)) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_8]).
% 0.55/1.00 cnf('0.12.0.0',axiom,
% 0.55/1.00 ( and(X1,X2) = and(X2,X1) ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008')).
% 0.55/1.00 cnf('0.12.1.0',plain,
% 0.55/1.00 ( and(X1,X2) = and(X2,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.55/1.00 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.55/1.00 cnf('0.12.1.1',plain,
% 0.55/1.00 ( and_star(X1,X2) = and(X2,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.12.1.0','0.7.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.12.1.2',plain,
% 0.55/1.00 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.12.1.1','0.7.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.12.2.0',plain,
% 0.55/1.00 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.55/1.00 inference(activate,[status(thm)],['0.12.1.2']),
% 0.55/1.00 [equation_3]).
% 0.55/1.00 cnf('0.15.0.0',plain,
% 0.55/1.00 ( or(truth,X1) = implies(falsehood,X1) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.5.2.0','0.8.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.15.1.0',plain,
% 0.55/1.00 ( or(truth,X1) = implies(falsehood,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.55/1.00 [weight('<27,8,5,[0,0,0,1]>')]).
% 0.55/1.00 cnf('0.15.2.0',plain,
% 0.55/1.00 ( implies(falsehood,X1) = or(truth,X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_11]).
% 0.55/1.00 cnf('0.16.0.0',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and(X1,X2) ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.6.2.0'])).
% 0.55/1.00 cnf('0.16.0.1',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and_star(X1,X2) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.16.0.0','0.7.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.16.1.0',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and_star(X1,X2) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.16.0.1']),
% 0.55/1.00 [weight('<69,6,7,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.16.2.0',plain,
% 0.55/1.00 ( not(or(not(X1),not(X2))) = and_star(X1,X2) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_12]).
% 0.55/1.00 cnf('0.17.0.0',plain,
% 0.55/1.00 ( and_star(truth,X1) = not(or(falsehood,not(X1))) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.16.2.0','0.8.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1.1','L')]).
% 0.55/1.00 cnf('0.17.1.0',plain,
% 0.55/1.00 ( and_star(truth,X1) = not(or(falsehood,not(X1))) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.55/1.00 [weight('<53,16,8,[1,0,0,2]>')]).
% 0.55/1.00 cnf('0.17.2.0',plain,
% 0.55/1.00 ( not(or(falsehood,not(X1))) = and_star(truth,X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_13]).
% 0.55/1.00 cnf('0.20.0.0',plain,
% 0.55/1.00 ( truth = implies(X1,implies(implies(X1,X2),implies(truth,X2))) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.3.2.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.20.0.1',plain,
% 0.55/1.00 ( truth = implies(X1,implies(implies(X1,X2),X2)) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.20.0.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('R.2.2','L')]).
% 0.55/1.00 cnf('0.20.1.0',plain,
% 0.55/1.00 ( truth = implies(X1,implies(implies(X1,X2),X2)) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.20.0.1']),
% 0.55/1.00 [weight('<71,3,1,[1,0,0,1]>')]).
% 0.55/1.00 cnf('0.20.2.0',plain,
% 0.55/1.00 ( implies(X1,implies(implies(X1,X2),X2)) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_16]).
% 0.55/1.00 cnf('0.21.0.0',plain,
% 0.55/1.00 ( truth = implies(implies(truth,X1),X1) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.20.2.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.21.0.1',plain,
% 0.55/1.00 ( truth = implies(X1,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.21.0.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('R.1','L')]).
% 0.55/1.00 cnf('0.21.1.0',plain,
% 0.55/1.00 ( truth = implies(X1,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.21.0.1']),
% 0.55/1.00 [weight('<19,20,1,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.21.2.0',plain,
% 0.55/1.00 ( implies(X1,X1) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_17]).
% 0.55/1.00 cnf('0.22.0.0',plain,
% 0.55/1.00 ( truth = or(truth,falsehood) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.21.2.0','0.15.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.22.1.0',plain,
% 0.55/1.00 ( truth = or(truth,falsehood) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.55/1.00 [weight('<19,21,15,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.22.1.1',plain,
% 0.55/1.00 ( truth = or(falsehood,truth) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.22.1.0','0.9.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.22.2.0',plain,
% 0.55/1.00 ( or(falsehood,truth) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.22.1.1',theory(equality)]),
% 0.55/1.00 [x,rule_18]).
% 0.55/1.00 cnf('0.23.0.0',plain,
% 0.55/1.00 ( truth = or(X1,not(X1)) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.21.2.0','0.5.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.23.1.0',plain,
% 0.55/1.00 ( truth = or(X1,not(X1)) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.55/1.00 [weight('<29,21,5,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.23.2.0',plain,
% 0.55/1.00 ( or(X1,not(X1)) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_19]).
% 0.55/1.00 cnf('0.26.0.0',plain,
% 0.55/1.00 ( or(falsehood,or(truth,X1)) = or(truth,X1) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.10.2.0','0.22.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.26.1.0',plain,
% 0.55/1.00 ( or(falsehood,or(truth,X1)) = or(truth,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.55/1.00 [weight('<53,22,10,[0,0,0,1]>')]).
% 0.55/1.00 cnf('0.26.2.0',plain,
% 0.55/1.00 ( or(falsehood,or(truth,X1)) = or(truth,X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_22]).
% 0.55/1.00 cnf('0.28.0.0',plain,
% 0.55/1.00 ( or(truth,X1) = or(falsehood,or(X1,truth)) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.26.2.0','0.9.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.2','L')]).
% 0.55/1.00 cnf('0.28.1.0',plain,
% 0.55/1.00 ( or(truth,X1) = or(falsehood,or(X1,truth)) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.55/1.00 [weight('<53,26,9,[1,0,0,2]>')]).
% 0.55/1.00 cnf('0.28.2.0',plain,
% 0.55/1.00 ( or(falsehood,or(X1,truth)) = or(truth,X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_24]).
% 0.55/1.00 cnf('0.54.0.0',plain,
% 0.55/1.00 ( truth = implies(X1,implies(implies(X2,X1),X1)) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.20.2.0','0.2.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.2','L')]).
% 0.55/1.00 cnf('0.54.1.0',plain,
% 0.55/1.00 ( truth = implies(X1,implies(implies(X2,X1),X1)) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.54.0.0']),
% 0.55/1.00 [weight('<71,20,2,[1,0,0,2]>')]).
% 0.55/1.00 cnf('0.54.2.0',plain,
% 0.55/1.00 ( implies(X1,implies(implies(X2,X1),X1)) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_47]).
% 0.55/1.00 cnf('0.55.0.0',plain,
% 0.55/1.00 ( truth = implies(X1,implies(X1,X1)) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.54.2.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.2.1','L')]).
% 0.55/1.00 cnf('0.55.0.1',plain,
% 0.55/1.00 ( truth = implies(X1,truth) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.55.0.0','0.21.2.0',theory(equality)]),
% 0.55/1.00 [pos('R.2','L')]).
% 0.55/1.00 cnf('0.55.1.0',plain,
% 0.55/1.00 ( truth = implies(X1,truth) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.55.0.1']),
% 0.55/1.00 [weight('<19,54,1,[1,0,0,3]>')]).
% 0.55/1.00 cnf('0.55.2.0',plain,
% 0.55/1.00 ( implies(X1,truth) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_48]).
% 0.55/1.00 cnf('0.56.0.0',plain,
% 0.55/1.00 ( truth = or(X1,truth) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.55.2.0','0.5.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.56.1.0',plain,
% 0.55/1.00 ( truth = or(X1,truth) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.55/1.00 [weight('<19,55,5,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.56.2.0',plain,
% 0.55/1.00 ( or(X1,truth) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_49]).
% 0.55/1.00 cnf('0.57.0.0',plain,
% 0.55/1.00 ( or(falsehood,or(X1,truth)) = or(truth,X1) ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.28.2.0'])).
% 0.55/1.00 cnf('0.57.0.1',plain,
% 0.55/1.00 ( or(falsehood,truth) = or(truth,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.57.0.0','0.56.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.2','L')]).
% 0.55/1.00 cnf('0.57.0.2',plain,
% 0.55/1.00 ( truth = or(truth,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.57.0.1','0.56.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.57.1.0',plain,
% 0.55/1.00 ( truth = or(truth,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.57.0.2']),
% 0.55/1.00 [weight('<19,28,56,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.57.2.0',plain,
% 0.55/1.00 ( or(truth,X1) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_50]).
% 0.55/1.00 cnf('0.58.0.0',plain,
% 0.55/1.00 ( implies(falsehood,X1) = or(truth,X1) ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.15.2.0'])).
% 0.55/1.00 cnf('0.58.0.1',plain,
% 0.55/1.00 ( implies(falsehood,X1) = truth ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.58.0.0','0.57.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.58.1.0',plain,
% 0.55/1.00 ( implies(falsehood,X1) = truth ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.58.0.1']),
% 0.55/1.00 [weight('<19,15,57,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.58.2.0',plain,
% 0.55/1.00 ( implies(falsehood,X1) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_51]).
% 0.55/1.00 cnf('0.60.0.0',plain,
% 0.55/1.00 ( implies(implies(X1,falsehood),falsehood) = implies(truth,X1) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.2.2.0','0.58.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.60.0.1',plain,
% 0.55/1.00 ( implies(implies(X1,falsehood),falsehood) = X1 ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.60.0.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.60.1.0',plain,
% 0.55/1.00 ( implies(implies(X1,falsehood),falsehood) = X1 ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.60.0.1']),
% 0.55/1.00 [weight('<41,58,2,[0,0,0,1]>')]).
% 0.55/1.00 cnf('0.60.2.0',plain,
% 0.55/1.00 ( implies(implies(X1,falsehood),falsehood) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_53]).
% 0.55/1.00 cnf('0.63.0.0',plain,
% 0.55/1.00 ( not(X1) = implies(or(X1,falsehood),falsehood) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.60.2.0','0.5.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.63.1.0',plain,
% 0.55/1.00 ( not(X1) = implies(or(X1,falsehood),falsehood) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.63.0.0']),
% 0.55/1.00 [weight('<47,60,5,[1,0,0,1]>')]).
% 0.55/1.00 cnf('0.63.2.0',plain,
% 0.55/1.00 ( implies(or(X1,falsehood),falsehood) = not(X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_56]).
% 0.55/1.00 cnf('0.64.0.0',plain,
% 0.55/1.00 ( not(X1) = implies(or(falsehood,X1),falsehood) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.63.2.0','0.9.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.64.1.0',plain,
% 0.55/1.00 ( not(X1) = implies(or(falsehood,X1),falsehood) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.64.0.0']),
% 0.55/1.00 [weight('<47,63,9,[1,0,0,1]>')]).
% 0.55/1.00 cnf('0.64.2.0',plain,
% 0.55/1.00 ( implies(or(falsehood,X1),falsehood) = not(X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_57]).
% 0.55/1.00 cnf('0.65.0.0',plain,
% 0.55/1.00 ( not(not(falsehood)) = implies(truth,falsehood) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.64.2.0','0.23.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.65.0.1',plain,
% 0.55/1.00 ( not(not(falsehood)) = falsehood ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.65.0.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.65.1.0',plain,
% 0.55/1.00 ( not(not(falsehood)) = falsehood ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.65.0.1']),
% 0.55/1.00 [weight('<19,64,23,[1,0,0,1]>')]).
% 0.55/1.00 cnf('0.65.2.0',plain,
% 0.55/1.00 ( not(not(falsehood)) = falsehood ),
% 0.55/1.00 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_58]).
% 0.55/1.00 cnf('0.66.0.0',plain,
% 0.55/1.00 ( or(not(falsehood),X1) = implies(falsehood,X1) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.5.2.0','0.65.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.66.0.1',plain,
% 0.55/1.00 ( or(not(falsehood),X1) = truth ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.66.0.0','0.58.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.66.1.0',plain,
% 0.55/1.00 ( or(not(falsehood),X1) = truth ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.66.0.1']),
% 0.55/1.00 [weight('<29,65,5,[0,0,0,1]>')]).
% 0.55/1.00 cnf('0.66.2.0',plain,
% 0.55/1.00 ( or(not(falsehood),X1) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_59]).
% 0.55/1.00 cnf('0.197.0.0',plain,
% 0.55/1.00 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.4.2.0'])).
% 0.55/1.00 cnf('0.197.0.1',plain,
% 0.55/1.00 ( implies(or(X1,not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.197.0.0','0.5.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.197.1.0',plain,
% 0.55/1.00 ( implies(or(X1,not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.197.0.1']),
% 0.55/1.00 [weight('<89,4,5,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.197.2.0',plain,
% 0.55/1.00 ( implies(or(X1,not(X2)),implies(X2,X1)) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.197.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_189]).
% 0.55/1.00 cnf('0.198.0.0',plain,
% 0.55/1.00 ( truth = implies(truth,implies(X1,not(falsehood))) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.197.2.0','0.66.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.198.0.1',plain,
% 0.55/1.00 ( truth = implies(X1,not(falsehood)) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.198.0.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.198.1.0',plain,
% 0.55/1.00 ( truth = implies(X1,not(falsehood)) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.198.0.1']),
% 0.55/1.00 [weight('<29,197,66,[1,0,0,1]>')]).
% 0.55/1.00 cnf('0.198.2.0',plain,
% 0.55/1.00 ( implies(X1,not(falsehood)) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.198.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_190]).
% 0.55/1.00 cnf('0.199.0.0',plain,
% 0.55/1.00 ( truth = not(falsehood) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.198.2.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.199.1.0',plain,
% 0.55/1.00 ( truth = not(falsehood) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.199.0.0']),
% 0.55/1.00 [weight('<11,198,1,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.199.2.0',plain,
% 0.55/1.00 ( not(falsehood) = truth ),
% 0.55/1.00 inference(orient,[status(thm)],['0.199.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_191]).
% 0.55/1.00 cnf('0.200.0.0',plain,
% 0.55/1.00 ( or(falsehood,X1) = implies(truth,X1) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.5.2.0','0.199.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.200.0.1',plain,
% 0.55/1.00 ( or(falsehood,X1) = X1 ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.200.0.0','0.1.2.0',theory(equality)]),
% 0.55/1.00 [pos('R','L')]).
% 0.55/1.00 cnf('0.200.1.0',plain,
% 0.55/1.00 ( or(falsehood,X1) = X1 ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.200.0.1']),
% 0.55/1.00 [weight('<19,199,5,[0,0,0,1]>')]).
% 0.55/1.00 cnf('0.200.2.0',plain,
% 0.55/1.00 ( or(falsehood,X1) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.200.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_192]).
% 0.55/1.00 cnf('0.203.0.0',plain,
% 0.55/1.00 ( X1 = or(X1,falsehood) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.200.2.0','0.9.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.203.1.0',plain,
% 0.55/1.00 ( X1 = or(X1,falsehood) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.203.0.0']),
% 0.55/1.00 [weight('<19,200,9,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.203.2.0',plain,
% 0.55/1.00 ( or(X1,falsehood) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.203.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_195]).
% 0.55/1.00 cnf('0.205.0.0',plain,
% 0.55/1.00 ( implies(or(X1,falsehood),falsehood) = not(X1) ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.63.2.0'])).
% 0.55/1.00 cnf('0.205.0.1',plain,
% 0.55/1.00 ( implies(X1,falsehood) = not(X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.205.0.0','0.203.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.205.1.0',plain,
% 0.55/1.00 ( implies(X1,falsehood) = not(X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.205.0.1']),
% 0.55/1.00 [weight('<23,63,203,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.205.2.0',plain,
% 0.55/1.00 ( implies(X1,falsehood) = not(X1) ),
% 0.55/1.00 inference(orient,[status(thm)],['0.205.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_197]).
% 0.55/1.00 cnf('0.206.0.0',plain,
% 0.55/1.00 ( implies(implies(X1,falsehood),falsehood) = X1 ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.60.2.0'])).
% 0.55/1.00 cnf('0.206.0.1',plain,
% 0.55/1.00 ( not(implies(X1,falsehood)) = X1 ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.206.0.0','0.205.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.206.0.2',plain,
% 0.55/1.00 ( not(not(X1)) = X1 ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.206.0.1','0.205.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.206.1.0',plain,
% 0.55/1.00 ( not(not(X1)) = X1 ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.206.0.2']),
% 0.55/1.00 [weight('<19,60,205,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.206.2.0',plain,
% 0.55/1.00 ( not(not(X1)) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.206.1.0',theory(equality)]),
% 0.55/1.00 [u,rule_198]).
% 0.55/1.00 cnf('0.207.0.0',plain,
% 0.55/1.00 ( not(or(falsehood,not(X1))) = and_star(truth,X1) ),
% 0.55/1.00 inference(interreduction_right,[status(thm)],['0.17.2.0'])).
% 0.55/1.00 cnf('0.207.0.1',plain,
% 0.55/1.00 ( not(not(X1)) = and_star(truth,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.207.0.0','0.200.2.0',theory(equality)]),
% 0.55/1.00 [pos('L.1','L')]).
% 0.55/1.00 cnf('0.207.1.0',plain,
% 0.55/1.00 ( not(not(X1)) = and_star(truth,X1) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.207.0.1']),
% 0.55/1.00 [weight('<27,17,200,[0,0,0,0]>')]).
% 0.55/1.00 cnf('0.207.1.1',plain,
% 0.55/1.00 ( X1 = and_star(truth,X1) ),
% 0.55/1.00 inference(reduction,[status(thm)],['0.207.1.0','0.206.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.207.2.0',plain,
% 0.55/1.00 ( and_star(truth,X1) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.207.1.1',theory(equality)]),
% 0.55/1.00 [x,rule_199]).
% 0.55/1.00 cnf('0.208.0.0',plain,
% 0.55/1.00 ( X1 = and_star(X1,truth) ),
% 0.55/1.00 inference(cp,[status(thm)],['0.207.2.0','0.12.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('0.208.1.0',plain,
% 0.55/1.00 ( X1 = and_star(X1,truth) ),
% 0.55/1.00 inference(weigh,[status(thm)],['0.208.0.0']),
% 0.55/1.00 [weight('<19,207,12,[1,0,0,0]>')]).
% 0.55/1.00 cnf('0.208.2.0',plain,
% 0.55/1.00 ( and_star(X1,truth) = X1 ),
% 0.55/1.00 inference(orient,[status(thm)],['0.208.1.0',theory(equality)]),
% 0.55/1.00 [x,rule_200]).
% 0.55/1.00 cnf('1.0.0.0',conjecture,
% 0.55/1.00 ( and_star(x,truth) = x ),
% 0.55/1.00 file('/tmp/WALDMEISTER_16825_n008',conjecture_1)).
% 0.55/1.00 cnf('1.0.0.1',plain,
% 0.55/1.00 ( x = x ),
% 0.55/1.00 inference(reduction,[status(thm)],['1.0.0.0','0.208.2.0',theory(equality)]),
% 0.55/1.00 [pos('L','L')]).
% 0.55/1.00 cnf('1.0.0.2',plain,
% 0.55/1.00 ( $true ),
% 0.55/1.00 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.55/1.00 [conjecture_1]).
% 0.55/1.00
% 0.55/1.00 Proved Goals:
% 0.55/1.00 No. 1: and_star(x,truth) ?= x joined, current: x = x
% 0.55/1.00 1 goal was specified, which was proved.
% 0.55/1.00 % SZS output end CNFRefutation
% 0.55/1.00 #END OF PROOF
% 0.55/1.00
% 0.55/1.00 Problem WALDMEISTER_16825_n008
% 0.55/1.00 CPs.gen 5373
% 0.55/1.00 CPs.reexp 0
% 0.55/1.00 Select 680
% 0.55/1.00 R 200
% 0.55/1.00 E 8
% 0.55/1.00 vsize 6.7M
% 0.55/1.00 rss 4.1M
% 0.55/1.00 process.time 0.039s
% 0.55/1.00 wallclock.time 0.039s
% 0.55/1.00 status S
% 0.55/1.00
% 0.55/1.00
% 0.55/1.00 Waldmeister states: Goal proved.
% 0.55/1.00 % SZS status Unsatisfiable
%------------------------------------------------------------------------------