%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n032.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 : Thu Jul 14 23:52:48 EDT 2022
% Result : Unsatisfiable 0.41s 0.85s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.10 % Command : woody %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Wed Jun 1 16:28:29 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.41/0.82 ********************************************************************************
% 0.41/0.82 * W A L D M E I S T E R \| \ / \|/ *
% 0.41/0.82 * |/ | \/ | *
% 0.41/0.82 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.41/0.82 * A. Jaeger and B. Loechner | | *
% 0.41/0.82 * <waldmeister@informatik.uni-kl.de> | *
% 0.41/0.82 ********************************************************************************
% 0.41/0.82
% 0.41/0.82
% 0.41/0.82 Goals:
% 0.41/0.82 ------
% 0.41/0.82
% 0.41/0.82 ( 1) add(add(a,b),c) ?=? add(a,add(b,c))
% 0.41/0.82
% 0.41/0.82 Detected structure: BoolescheAlgebra
% 0.41/0.82 ********************************************************************************
% 0.41/0.82 ****************************** COMPLETION - PROOF ******************************
% 0.41/0.82 ********************************************************************************
% 0.41/0.82
% 0.41/0.85 joined goal: 1 add(add(a,b),c) ?= add(a,add(b,c)) to add(a,add(c,b))
% 0.41/0.85 goal joined
% 0.41/0.85 % SZS status Unsatisfiable
% 0.41/0.85 #START OF PROOF
% 0.41/0.85 % SZS output start CNFRefutation
% 0.41/0.85 cnf('0.2.0.0',axiom,
% 0.41/0.85 ( X1 = add(X1,additive_identity) ),
% 0.41/0.85 file('/tmp/WALDMEISTER_2699_n032')).
% 0.41/0.85 cnf('0.2.1.0',plain,
% 0.41/0.85 ( X1 = add(X1,additive_identity) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.41/0.85 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.41/0.85 cnf('0.2.2.0',plain,
% 0.41/0.85 ( add(X1,additive_identity) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_2]).
% 0.41/0.85 cnf('0.3.0.0',axiom,
% 0.41/0.85 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.41/0.85 file('/tmp/WALDMEISTER_2699_n032')).
% 0.41/0.85 cnf('0.3.1.0',plain,
% 0.41/0.85 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.41/0.85 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.41/0.85 cnf('0.3.2.0',plain,
% 0.41/0.85 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.41/0.85 inference(activate,[status(thm)],['0.3.1.0']),
% 0.41/0.85 [equation_1]).
% 0.41/0.85 cnf('0.4.0.0',axiom,
% 0.41/0.85 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.41/0.85 file('/tmp/WALDMEISTER_2699_n032')).
% 0.41/0.85 cnf('0.4.1.0',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.41/0.85 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.41/0.85 cnf('0.4.2.0',plain,
% 0.41/0.85 ( add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_3]).
% 0.41/0.85 cnf('0.5.0.0',axiom,
% 0.41/0.85 ( multiply(X1,inverse(X1)) = additive_identity ),
% 0.41/0.85 file('/tmp/WALDMEISTER_2699_n032')).
% 0.41/0.85 cnf('0.5.1.0',plain,
% 0.41/0.85 ( multiply(X1,inverse(X1)) = additive_identity ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.41/0.85 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.41/0.85 cnf('0.5.2.0',plain,
% 0.41/0.85 ( multiply(X1,inverse(X1)) = additive_identity ),
% 0.41/0.85 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_4]).
% 0.41/0.85 cnf('0.6.0.0',axiom,
% 0.41/0.85 ( multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)) ),
% 0.41/0.85 file('/tmp/WALDMEISTER_2699_n032')).
% 0.41/0.85 cnf('0.6.1.0',plain,
% 0.41/0.85 ( multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.41/0.85 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.41/0.85 cnf('0.6.2.0',plain,
% 0.41/0.85 ( multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_5]).
% 0.41/0.85 cnf('0.7.0.0',axiom,
% 0.41/0.85 ( add(X1,X2) = add(X2,X1) ),
% 0.41/0.85 file('/tmp/WALDMEISTER_2699_n032')).
% 0.41/0.85 cnf('0.7.1.0',plain,
% 0.41/0.85 ( add(X1,X2) = add(X2,X1) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.41/0.85 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.41/0.85 cnf('0.7.2.0',plain,
% 0.41/0.85 ( add(X1,X2) = add(X2,X1) ),
% 0.41/0.85 inference(activate,[status(thm)],['0.7.1.0']),
% 0.41/0.85 [equation_2]).
% 0.41/0.85 cnf('0.11.0.0',plain,
% 0.41/0.85 ( add(additive_identity,X1) = X1 ),
% 0.41/0.85 inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
% 0.41/0.85 [pos('L','L')]).
% 0.41/0.85 cnf('0.11.1.0',plain,
% 0.41/0.85 ( add(additive_identity,X1) = X1 ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.41/0.85 [weight('<3,7,2,[1,0,0,0]>')]).
% 0.41/0.85 cnf('0.11.2.0',plain,
% 0.41/0.85 ( add(additive_identity,X1) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_9]).
% 0.41/0.85 cnf('0.13.0.0',plain,
% 0.41/0.85 ( add(X1,multiply(additive_identity,X2)) = multiply(X1,add(X1,X2)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.1','L')]).
% 0.41/0.85 cnf('0.13.1.0',plain,
% 0.41/0.85 ( add(X1,multiply(additive_identity,X2)) = multiply(X1,add(X1,X2)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.41/0.85 [weight('<5,6,2,[1,0,0,1]>')]).
% 0.41/0.85 cnf('0.13.2.0',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = add(X1,multiply(additive_identity,X2)) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_11]).
% 0.41/0.85 cnf('0.14.0.0',plain,
% 0.41/0.85 ( add(X1,multiply(additive_identity,X2)) = multiply(X1,add(X2,X1)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.13.2.0','0.7.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.2','L')]).
% 0.41/0.85 cnf('0.14.1.0',plain,
% 0.41/0.85 ( add(X1,multiply(additive_identity,X2)) = multiply(X1,add(X2,X1)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.41/0.85 [weight('<5,13,7,[1,0,0,2]>')]).
% 0.41/0.85 cnf('0.14.2.0',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X1)) = add(X1,multiply(additive_identity,X2)) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_12]).
% 0.41/0.85 cnf('0.18.0.0',plain,
% 0.41/0.85 ( multiply(X1,add(inverse(X1),X2)) = add(additive_identity,multiply(X1,X2)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.4.2.0','0.5.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.1','L')]).
% 0.41/0.85 cnf('0.18.1.0',plain,
% 0.41/0.85 ( multiply(X1,add(inverse(X1),X2)) = add(additive_identity,multiply(X1,X2)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.41/0.85 [weight('<6,5,4,[0,0,0,1]>')]).
% 0.41/0.85 cnf('0.18.1.1',plain,
% 0.41/0.85 ( multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2) ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.18.1.0','0.11.2.0',theory(equality)]),
% 0.41/0.85 [pos('R','L')]).
% 0.41/0.85 cnf('0.18.2.0',plain,
% 0.41/0.85 ( multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.18.1.1',theory(equality)]),
% 0.41/0.85 [u,rule_16]).
% 0.41/0.85 cnf('0.19.0.0',plain,
% 0.41/0.85 ( multiply(X1,additive_identity) = multiply(X1,inverse(X1)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.18.2.0','0.2.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.2','L')]).
% 0.41/0.85 cnf('0.19.0.1',plain,
% 0.41/0.85 ( multiply(X1,additive_identity) = additive_identity ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.19.0.0','0.5.2.0',theory(equality)]),
% 0.41/0.85 [pos('R','L')]).
% 0.41/0.85 cnf('0.19.1.0',plain,
% 0.41/0.85 ( multiply(X1,additive_identity) = additive_identity ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.19.0.1']),
% 0.41/0.85 [weight('<3,18,2,[1,0,0,2]>')]).
% 0.41/0.85 cnf('0.19.2.0',plain,
% 0.41/0.85 ( multiply(X1,additive_identity) = additive_identity ),
% 0.41/0.85 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_17]).
% 0.41/0.85 cnf('0.21.0.0',plain,
% 0.41/0.85 ( additive_identity = multiply(additive_identity,X1) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.19.2.0','0.3.2.0',theory(equality)]),
% 0.41/0.85 [pos('L','L')]).
% 0.41/0.85 cnf('0.21.1.0',plain,
% 0.41/0.85 ( additive_identity = multiply(additive_identity,X1) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.41/0.85 [weight('<3,19,3,[1,0,0,0]>')]).
% 0.41/0.85 cnf('0.21.2.0',plain,
% 0.41/0.85 ( multiply(additive_identity,X1) = additive_identity ),
% 0.41/0.85 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_19]).
% 0.41/0.85 cnf('0.23.0.0',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = add(X1,multiply(additive_identity,X2)) ),
% 0.41/0.85 inference(interreduction_right,[status(thm)],['0.13.2.0'])).
% 0.41/0.85 cnf('0.23.0.1',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = add(X1,additive_identity) ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.23.0.0','0.21.2.0',theory(equality)]),
% 0.41/0.85 [pos('R.2','L')]).
% 0.41/0.85 cnf('0.23.0.2',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = X1 ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.23.0.1','0.2.2.0',theory(equality)]),
% 0.41/0.85 [pos('R','L')]).
% 0.41/0.85 cnf('0.23.1.0',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = X1 ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.23.0.2']),
% 0.41/0.85 [weight('<5,13,21,[0,0,0,0]>')]).
% 0.41/0.85 cnf('0.23.2.0',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_21]).
% 0.41/0.85 cnf('0.24.0.0',plain,
% 0.41/0.85 ( X1 = multiply(X1,X1) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.23.2.0','0.2.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.2','L')]).
% 0.41/0.85 cnf('0.24.1.0',plain,
% 0.41/0.85 ( X1 = multiply(X1,X1) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.41/0.85 [weight('<3,23,2,[1,0,0,2]>')]).
% 0.41/0.85 cnf('0.24.2.0',plain,
% 0.41/0.85 ( multiply(X1,X1) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_22]).
% 0.41/0.85 cnf('0.25.0.0',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X1)) = add(X1,multiply(additive_identity,X2)) ),
% 0.41/0.85 inference(interreduction_right,[status(thm)],['0.14.2.0'])).
% 0.41/0.85 cnf('0.25.0.1',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X1)) = add(X1,additive_identity) ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.25.0.0','0.21.2.0',theory(equality)]),
% 0.41/0.85 [pos('R.2','L')]).
% 0.41/0.85 cnf('0.25.0.2',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X1)) = X1 ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.25.0.1','0.2.2.0',theory(equality)]),
% 0.41/0.85 [pos('R','L')]).
% 0.41/0.85 cnf('0.25.1.0',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X1)) = X1 ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.25.0.2']),
% 0.41/0.85 [weight('<5,14,21,[0,0,0,0]>')]).
% 0.41/0.85 cnf('0.25.2.0',plain,
% 0.41/0.85 ( multiply(X1,add(X2,X1)) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_23]).
% 0.41/0.85 cnf('0.27.0.0',plain,
% 0.41/0.85 ( multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.4.2.0','0.24.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.1','L')]).
% 0.41/0.85 cnf('0.27.0.1',plain,
% 0.41/0.85 ( X1 = add(X1,multiply(X1,X2)) ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.27.0.0','0.23.2.0',theory(equality)]),
% 0.41/0.85 [pos('L','L')]).
% 0.41/0.85 cnf('0.27.1.0',plain,
% 0.41/0.85 ( X1 = add(X1,multiply(X1,X2)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.27.0.1']),
% 0.41/0.85 [weight('<5,24,4,[0,0,0,1]>')]).
% 0.41/0.85 cnf('0.27.2.0',plain,
% 0.41/0.85 ( add(X1,multiply(X1,X2)) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_25]).
% 0.41/0.85 cnf('0.29.0.0',plain,
% 0.41/0.85 ( X1 = add(X1,multiply(X2,X1)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.27.2.0','0.3.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.2','L')]).
% 0.41/0.85 cnf('0.29.1.0',plain,
% 0.41/0.85 ( X1 = add(X1,multiply(X2,X1)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.41/0.85 [weight('<5,27,3,[1,0,0,2]>')]).
% 0.41/0.85 cnf('0.29.2.0',plain,
% 0.41/0.85 ( add(X1,multiply(X2,X1)) = X1 ),
% 0.41/0.85 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_27]).
% 0.41/0.85 cnf('0.31.0.0',plain,
% 0.41/0.85 ( add(X1,X2) = add(add(X1,X2),X1) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.29.2.0','0.23.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.2','L')]).
% 0.41/0.85 cnf('0.31.1.0',plain,
% 0.41/0.85 ( add(X1,X2) = add(add(X1,X2),X1) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.41/0.85 [weight('<5,29,23,[1,0,0,2]>')]).
% 0.41/0.85 cnf('0.31.1.1',plain,
% 0.41/0.85 ( add(X1,X2) = add(X1,add(X1,X2)) ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.31.1.0','0.7.2.0',theory(equality)]),
% 0.41/0.85 [pos('R','L')]).
% 0.41/0.85 cnf('0.31.2.0',plain,
% 0.41/0.85 ( add(X1,add(X1,X2)) = add(X1,X2) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.31.1.1',theory(equality)]),
% 0.41/0.85 [x,rule_29]).
% 0.41/0.85 cnf('0.57.0.0',plain,
% 0.41/0.85 ( add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X1,X3)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.6.2.0','0.7.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.1','L')]).
% 0.41/0.85 cnf('0.57.1.0',plain,
% 0.41/0.85 ( add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X1,X3)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.57.0.0']),
% 0.41/0.85 [weight('<7,7,6,[0,0,0,1]>')]).
% 0.41/0.85 cnf('0.57.2.0',plain,
% 0.41/0.85 ( multiply(add(X1,X2),add(X2,X3)) = add(X2,multiply(X1,X3)) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.41/0.85 [x,rule_55]).
% 0.41/0.85 cnf('0.69.0.0',plain,
% 0.41/0.85 ( add(X1,multiply(add(X1,X2),X3)) = multiply(add(X1,X2),add(X1,X3)) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.6.2.0','0.31.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.1','L')]).
% 0.41/0.85 cnf('0.69.0.1',plain,
% 0.41/0.85 ( add(X1,multiply(add(X1,X2),X3)) = add(X1,multiply(X2,X3)) ),
% 0.41/0.85 inference(reduction,[status(thm)],['0.69.0.0','0.6.2.0',theory(equality)]),
% 0.41/0.85 [pos('R','L')]).
% 0.41/0.85 cnf('0.69.1.0',plain,
% 0.41/0.85 ( add(X1,multiply(add(X1,X2),X3)) = add(X1,multiply(X2,X3)) ),
% 0.41/0.85 inference(weigh,[status(thm)],['0.69.0.1']),
% 0.41/0.85 [weight('<7,31,6,[0,0,0,1]>')]).
% 0.41/0.85 cnf('0.69.2.0',plain,
% 0.41/0.85 ( add(X1,multiply(add(X1,X2),X3)) = add(X1,multiply(X2,X3)) ),
% 0.41/0.85 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 0.41/0.85 [u,rule_67]).
% 0.41/0.85 cnf('0.111.0.0',plain,
% 0.41/0.85 ( add(X1,multiply(X2,add(X2,X3))) = add(X1,add(X2,multiply(X1,X3))) ),
% 0.41/0.85 inference(cp,[status(thm)],['0.69.2.0','0.57.2.0',theory(equality)]),
% 0.41/0.85 [pos('L.2','L')]).
% 0.41/0.85 cnf('0.111.0.1',plain,
% 0.41/0.85 ( add(X1,X2) = add(X1,add(X2,multiply(X1,X3))) ),
% 0.44/0.85 inference(reduction,[status(thm)],['0.111.0.0','0.23.2.0',theory(equality)]),
% 0.44/0.85 [pos('L.2','L')]).
% 0.44/0.85 cnf('0.111.1.0',plain,
% 0.44/0.85 ( add(X1,X2) = add(X1,add(X2,multiply(X1,X3))) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.111.0.1']),
% 0.44/0.85 [weight('<7,69,57,[1,0,0,2]>')]).
% 0.44/0.85 cnf('0.111.2.0',plain,
% 0.44/0.85 ( add(X1,add(X2,multiply(X1,X3))) = add(X1,X2) ),
% 0.44/0.85 inference(orient,[status(thm)],['0.111.1.0',theory(equality)]),
% 0.44/0.85 [x,rule_109]).
% 0.44/0.85 cnf('0.122.0.0',plain,
% 0.44/0.85 ( add(X1,X2) = add(X1,add(X2,multiply(X3,X1))) ),
% 0.44/0.85 inference(cp,[status(thm)],['0.111.2.0','0.3.2.0',theory(equality)]),
% 0.44/0.85 [pos('L.2.2','L')]).
% 0.44/0.85 cnf('0.122.1.0',plain,
% 0.44/0.85 ( add(X1,X2) = add(X1,add(X2,multiply(X3,X1))) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.122.0.0']),
% 0.44/0.85 [weight('<7,111,3,[1,0,0,4]>')]).
% 0.44/0.85 cnf('0.122.2.0',plain,
% 0.44/0.85 ( add(X1,add(X2,multiply(X3,X1))) = add(X1,X2) ),
% 0.44/0.85 inference(orient,[status(thm)],['0.122.1.0',theory(equality)]),
% 0.44/0.85 [x,rule_120]).
% 0.44/0.85 cnf('0.127.0.0',plain,
% 0.44/0.85 ( add(X1,X2) = add(X1,add(multiply(X3,X1),X2)) ),
% 0.44/0.85 inference(cp,[status(thm)],['0.122.2.0','0.7.2.0',theory(equality)]),
% 0.44/0.85 [pos('L.2','L')]).
% 0.44/0.85 cnf('0.127.1.0',plain,
% 0.44/0.85 ( add(X1,X2) = add(X1,add(multiply(X3,X1),X2)) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.127.0.0']),
% 0.44/0.85 [weight('<7,122,7,[1,0,0,2]>')]).
% 0.44/0.85 cnf('0.127.2.0',plain,
% 0.44/0.85 ( add(X1,add(multiply(X2,X1),X3)) = add(X1,X3) ),
% 0.44/0.85 inference(orient,[status(thm)],['0.127.1.0',theory(equality)]),
% 0.44/0.85 [x,rule_125]).
% 0.44/0.85 cnf('0.128.0.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X1,X2),add(X3,X1)) ),
% 0.44/0.85 inference(cp,[status(thm)],['0.122.2.0','0.23.2.0',theory(equality)]),
% 0.44/0.85 [pos('L.2.2','L')]).
% 0.44/0.85 cnf('0.128.1.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X1,X2),add(X3,X1)) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.128.0.0']),
% 0.44/0.85 [weight('<7,122,23,[1,0,0,4]>')]).
% 0.44/0.85 cnf('0.128.2.0',plain,
% 0.44/0.85 ( add(add(X1,X2),add(X3,X1)) = add(add(X1,X2),X3) ),
% 0.44/0.85 inference(orient,[status(thm)],['0.128.1.0',theory(equality)]),
% 0.44/0.85 [x,rule_126]).
% 0.44/0.85 cnf('0.135.0.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X1,X2),add(X2,X3)) ),
% 0.44/0.85 inference(cp,[status(thm)],['0.127.2.0','0.25.2.0',theory(equality)]),
% 0.44/0.85 [pos('L.2.1','L')]).
% 0.44/0.85 cnf('0.135.1.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X1,X2),add(X2,X3)) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.135.0.0']),
% 0.44/0.85 [weight('<7,127,25,[1,0,0,3]>')]).
% 0.44/0.85 cnf('0.135.2.0',plain,
% 0.44/0.85 ( add(add(X1,X2),add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.44/0.85 inference(orient,[status(thm)],['0.135.1.0',theory(equality)]),
% 0.44/0.85 [x,rule_132]).
% 0.44/0.85 cnf('0.136.0.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X3,X1),add(X1,X2)) ),
% 0.44/0.85 inference(cp,[status(thm)],['0.128.2.0','0.7.2.0',theory(equality)]),
% 0.44/0.85 [pos('L','L')]).
% 0.44/0.85 cnf('0.136.1.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X3,X1),add(X1,X2)) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.136.0.0']),
% 0.44/0.85 [weight('<7,128,7,[1,0,0,0]>')]).
% 0.44/0.85 cnf('0.136.1.1',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X3,X1),X2) ),
% 0.44/0.85 inference(reduction,[status(thm)],['0.136.1.0','0.135.2.0',theory(equality)]),
% 0.44/0.85 [pos('R','L')]).
% 0.44/0.85 cnf('0.136.2.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(add(X3,X1),X2) ),
% 0.44/0.85 inference(activate,[status(thm)],['0.136.1.1']),
% 0.44/0.85 [equation_4]).
% 0.44/0.85 cnf('0.137.0.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.44/0.85 inference(cp,[status(thm)],['0.136.2.0','0.7.2.0',theory(equality)]),
% 0.44/0.85 [pos('L','L')]).
% 0.44/0.85 cnf('0.137.1.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.44/0.85 inference(weigh,[status(thm)],['0.137.0.0']),
% 0.44/0.85 [weight('<5,136,7,[1,0,0,0]>')]).
% 0.44/0.85 cnf('0.137.2.0',plain,
% 0.44/0.85 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.44/0.85 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 0.44/0.85 [u,rule_133]).
% 0.44/0.85 cnf('1.0.0.0',conjecture,
% 0.44/0.85 ( add(add(a,b),c) = add(a,add(b,c)) ),
% 0.44/0.85 file('/tmp/WALDMEISTER_2699_n032',conjecture_1)).
% 0.44/0.85 cnf('1.0.0.1',plain,
% 0.44/0.85 ( add(a,add(b,c)) = add(a,add(b,c)) ),
% 0.44/0.85 inference(reduction,[status(thm)],['1.0.0.0','0.137.2.0',theory(equality)]),
% 0.44/0.85 [pos('L','L')]).
% 0.44/0.85 cnf('1.0.0.2',plain,
% 0.44/0.85 ( add(a,add(c,b)) = add(a,add(b,c)) ),
% 0.44/0.85 inference(reduction,[status(thm)],['1.0.0.1','0.7.2.0',theory(equality)]),
% 0.44/0.85 [pos('L.2','L')]).
% 0.44/0.85 cnf('1.0.0.3',plain,
% 0.44/0.85 ( add(a,add(c,b)) = add(a,add(c,b)) ),
% 0.44/0.85 inference(reduction,[status(thm)],['1.0.0.2','0.7.2.0',theory(equality)]),
% 0.44/0.85 [pos('R.2','L')]).
% 0.44/0.85 cnf('1.0.0.4',plain,
% 0.44/0.85 ( $true ),
% 0.44/0.85 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 0.44/0.85 [conjecture_1]).
% 0.44/0.85
% 0.44/0.85 Proved Goals:
% 0.44/0.85 No. 1: add(add(a,b),c) ?= add(a,add(b,c)) joined, current: add(a,add(c,b)) = add(a,add(c,b))
% 0.44/0.85 1 goal was specified, which was proved.
% 0.44/0.85 % SZS output end CNFRefutation
% 0.44/0.85 #END OF PROOF
% 0.44/0.85
% 0.44/0.85 Problem WALDMEISTER_2699_n032
% 0.44/0.85 CPs.gen 10977
% 0.44/0.85 CPs.reexp 0
% 0.44/0.85 Select 958
% 0.44/0.85 R 133
% 0.44/0.85 E 4
% 0.44/0.85 vsize 6.5M
% 0.44/0.85 rss 3.8M
% 0.44/0.85 process.time 0.030s
% 0.44/0.85 wallclock.time 0.030s
% 0.44/0.85 status S
% 0.44/0.85
% 0.44/0.85
% 0.44/0.85 Waldmeister states: Goal proved.
% 0.44/0.85 % SZS status Unsatisfiable
%------------------------------------------------------------------------------