TSTP Solution File: RNG021-6 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : RNG021-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n020.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 : Mon Jul 18 20:47:25 EDT 2022
% Result : Unsatisfiable 0.66s 1.04s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG021-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n020.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 : Mon May 30 16:40:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/1.04 ********************************************************************************
% 0.66/1.04 * W A L D M E I S T E R \| \ / \|/ *
% 0.66/1.04 * |/ | \/ | *
% 0.66/1.04 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.66/1.04 * A. Jaeger and B. Loechner | | *
% 0.66/1.04 * <waldmeister@informatik.uni-kl.de> | *
% 0.66/1.04 ********************************************************************************
% 0.66/1.04
% 0.66/1.04
% 0.66/1.04 Goals:
% 0.66/1.04 ------
% 0.66/1.04
% 0.66/1.04 ( 1) add(associator(u,x,y),associator(v,x,y)) ?=? associator(add(u,v),x,y)
% 0.66/1.04
% 0.66/1.04 Detected structure: NichtassoziativerRing
% 0.66/1.04 ********************************************************************************
% 0.66/1.04 ****************************** COMPLETION - PROOF ******************************
% 0.66/1.04 ********************************************************************************
% 0.66/1.04
% 0.66/1.04 joined goal: 1 add(associator(u,x,y),associator(v,x,y)) ?= associator(add(u,v),x,y) to add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y))))
% 0.66/1.04 goal joined
% 0.66/1.04 % SZS status Unsatisfiable
% 0.66/1.04 #START OF PROOF
% 0.66/1.04 % SZS output start CNFRefutation
% 0.66/1.04 cnf('0.2.0.0',axiom,
% 0.66/1.04 ( X1 = add(additive_identity,X1) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.2.1.0',plain,
% 0.66/1.04 ( X1 = add(additive_identity,X1) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.66/1.04 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.66/1.04 cnf('0.2.2.0',plain,
% 0.66/1.04 ( add(additive_identity,X1) = X1 ),
% 0.66/1.04 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.66/1.04 [x,rule_2]).
% 0.66/1.04 cnf('0.3.0.0',axiom,
% 0.66/1.04 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.3.1.0',plain,
% 0.66/1.04 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.66/1.04 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.66/1.04 cnf('0.3.2.0',plain,
% 0.66/1.04 ( additive_inverse(additive_inverse(X1)) = X1 ),
% 0.66/1.04 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.66/1.04 [x,rule_3]).
% 0.66/1.04 cnf('0.8.0.0',axiom,
% 0.66/1.04 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.8.1.0',plain,
% 0.66/1.04 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.66/1.04 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.66/1.04 cnf('0.8.2.0',plain,
% 0.66/1.04 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.66/1.04 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.66/1.04 [u,rule_8]).
% 0.66/1.04 cnf('0.10.0.0',axiom,
% 0.66/1.04 ( add(X1,X2) = add(X2,X1) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.10.1.0',plain,
% 0.66/1.04 ( add(X1,X2) = add(X2,X1) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.66/1.04 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.66/1.04 cnf('0.10.2.0',plain,
% 0.66/1.04 ( add(X1,X2) = add(X2,X1) ),
% 0.66/1.04 inference(activate,[status(thm)],['0.10.1.0']),
% 0.66/1.04 [equation_1]).
% 0.66/1.04 cnf('0.11.0.0',axiom,
% 0.66/1.04 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.11.1.0',plain,
% 0.66/1.04 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.66/1.04 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.66/1.04 cnf('0.11.2.0',plain,
% 0.66/1.04 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.66/1.04 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.66/1.04 [x,rule_10]).
% 0.66/1.04 cnf('0.12.0.0',axiom,
% 0.66/1.04 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.12.1.0',plain,
% 0.66/1.04 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.66/1.04 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.66/1.04 cnf('0.12.2.0',plain,
% 0.66/1.04 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.66/1.04 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.66/1.04 [u,rule_11]).
% 0.66/1.04 cnf('0.14.0.0',axiom,
% 0.66/1.04 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020')).
% 0.66/1.04 cnf('0.14.1.0',plain,
% 0.66/1.04 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.66/1.04 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.66/1.04 cnf('0.14.1.1',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) = associator(X1,X2,X3) ),
% 0.66/1.04 inference(reduction,[status(thm)],['0.14.1.0','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('L','L')]).
% 0.66/1.04 cnf('0.14.2.0',plain,
% 0.66/1.04 ( associator(X1,X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) ),
% 0.66/1.04 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 0.66/1.04 [x,rule_13]).
% 0.66/1.04 cnf('0.16.0.0',plain,
% 0.66/1.04 ( add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2) ),
% 0.66/1.04 inference(cp,[status(thm)],['0.11.2.0','0.12.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.1','L')]).
% 0.66/1.04 cnf('0.16.0.1',plain,
% 0.66/1.04 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.66/1.04 inference(reduction,[status(thm)],['0.16.0.0','0.2.2.0',theory(equality)]),
% 0.66/1.04 [pos('R','L')]).
% 0.66/1.04 cnf('0.16.1.0',plain,
% 0.66/1.04 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.16.0.1']),
% 0.66/1.04 [weight('<6,12,11,[0,0,0,1]>')]).
% 0.66/1.04 cnf('0.16.2.0',plain,
% 0.66/1.04 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.66/1.04 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.66/1.04 [u,rule_15]).
% 0.66/1.04 cnf('0.17.0.0',plain,
% 0.66/1.04 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.66/1.04 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.2.1','L')]).
% 0.66/1.04 cnf('0.17.1.0',plain,
% 0.66/1.04 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.66/1.04 [weight('<6,16,3,[1,0,0,3]>')]).
% 0.66/1.04 cnf('0.17.2.0',plain,
% 0.66/1.04 ( add(additive_inverse(X1),add(X1,X2)) = X2 ),
% 0.66/1.04 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.66/1.04 [x,rule_16]).
% 0.66/1.04 cnf('0.19.0.0',plain,
% 0.66/1.04 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.66/1.04 inference(cp,[status(thm)],['0.17.2.0','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.2','L')]).
% 0.66/1.04 cnf('0.19.1.0',plain,
% 0.66/1.04 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.66/1.04 [weight('<6,17,10,[1,0,0,3]>')]).
% 0.66/1.04 cnf('0.19.2.0',plain,
% 0.66/1.04 ( add(additive_inverse(X1),add(X2,X1)) = X2 ),
% 0.66/1.04 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.66/1.04 [x,rule_18]).
% 0.66/1.04 cnf('0.20.0.0',plain,
% 0.66/1.04 ( additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2) ),
% 0.66/1.04 inference(cp,[status(thm)],['0.19.2.0','0.17.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.2','L')]).
% 0.66/1.04 cnf('0.20.1.0',plain,
% 0.66/1.04 ( additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.66/1.04 [weight('<6,19,17,[1,0,0,3]>')]).
% 0.66/1.04 cnf('0.20.1.1',plain,
% 0.66/1.04 ( additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))) ),
% 0.66/1.04 inference(reduction,[status(thm)],['0.20.1.0','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('R','L')]).
% 0.66/1.04 cnf('0.20.2.0',plain,
% 0.66/1.04 ( add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2) ),
% 0.66/1.04 inference(orient,[status(thm)],['0.20.1.1',theory(equality)]),
% 0.66/1.04 [x,rule_19]).
% 0.66/1.04 cnf('0.21.0.0',plain,
% 0.66/1.04 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.66/1.04 inference(cp,[status(thm)],['0.17.2.0','0.20.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.2','L')]).
% 0.66/1.04 cnf('0.21.1.0',plain,
% 0.66/1.04 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.66/1.04 [weight('<4,20,17,[0,0,0,3]>')]).
% 0.66/1.04 cnf('0.21.2.0',plain,
% 0.66/1.04 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.66/1.04 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.66/1.04 [u,rule_20]).
% 0.66/1.04 cnf('0.35.0.0',plain,
% 0.66/1.04 ( add(X1,add(X2,X3)) = add(add(X2,X1),X3) ),
% 0.66/1.04 inference(cp,[status(thm)],['0.11.2.0','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.1','L')]).
% 0.66/1.04 cnf('0.35.0.1',plain,
% 0.66/1.04 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.66/1.04 inference(reduction,[status(thm)],['0.35.0.0','0.11.2.0',theory(equality)]),
% 0.66/1.04 [pos('R','L')]).
% 0.66/1.04 cnf('0.35.1.0',plain,
% 0.66/1.04 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.66/1.04 inference(weigh,[status(thm)],['0.35.0.1']),
% 0.66/1.04 [weight('<10,11,10,[1,0,0,1]>')]).
% 0.66/1.04 cnf('0.35.2.0',plain,
% 0.66/1.04 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.66/1.04 inference(activate,[status(thm)],['0.35.1.0']),
% 0.66/1.04 [equation_3]).
% 0.66/1.04 cnf('1.0.0.0',conjecture,
% 0.66/1.04 ( add(associator(u,x,y),associator(v,x,y)) = associator(add(u,v),x,y) ),
% 0.66/1.04 file('/tmp/WALDMEISTER_24309_n020',conjecture_1)).
% 0.66/1.04 cnf('1.0.0.1',plain,
% 0.66/1.04 ( add(associator(v,x,y),associator(u,x,y)) = associator(add(u,v),x,y) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.0','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('L','L')]).
% 0.66/1.04 cnf('1.0.0.2',plain,
% 0.66/1.04 ( add(add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y)),associator(u,x,y)) = associator(add(u,v),x,y) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.1','0.14.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.1','L')]).
% 0.66/1.04 cnf('1.0.0.3',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(v,x),y),associator(u,x,y))) = associator(add(u,v),x,y) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.2','0.11.2.0',theory(equality)]),
% 0.66/1.04 [pos('L','L')]).
% 0.66/1.04 cnf('1.0.0.4',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(v,x),y),add(additive_inverse(multiply(u,multiply(x,y))),multiply(multiply(u,x),y)))) = associator(add(u,v),x,y) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.3','0.14.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.2.2','L')]).
% 0.66/1.04 cnf('1.0.0.5',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = associator(add(u,v),x,y) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.4','0.35.2.0',theory(equality)]),
% 0.66/1.04 [pos('L.2','L')]).
% 0.66/1.04 cnf('1.0.0.6',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(multiply(add(u,v),multiply(x,y))),multiply(multiply(add(u,v),x),y)) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.5','0.14.2.0',theory(equality)]),
% 0.66/1.04 [pos('R','L')]).
% 0.66/1.04 cnf('1.0.0.7',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.6','0.8.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.1.1','L')]).
% 0.66/1.04 cnf('1.0.0.8',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(add(multiply(v,multiply(x,y)),multiply(u,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.7','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.1.1','L')]).
% 0.66/1.04 cnf('1.0.0.9',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(add(additive_inverse(multiply(u,multiply(x,y))),additive_inverse(multiply(v,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.8','0.21.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.1','L')]).
% 0.66/1.04 cnf('1.0.0.10',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(add(additive_inverse(multiply(v,multiply(x,y))),additive_inverse(multiply(u,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.9','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.1','L')]).
% 0.66/1.04 cnf('1.0.0.11',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),multiply(multiply(add(u,v),x),y))) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.10','0.11.2.0',theory(equality)]),
% 0.66/1.04 [pos('R','L')]).
% 0.66/1.04 cnf('1.0.0.12',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),multiply(add(multiply(u,x),multiply(v,x)),y))) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.11','0.8.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.2.2.1','L')]).
% 0.66/1.04 cnf('1.0.0.13',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),multiply(add(multiply(v,x),multiply(u,x)),y))) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.12','0.10.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.2.2.1','L')]).
% 0.66/1.04 cnf('1.0.0.14',plain,
% 0.66/1.04 ( add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) ),
% 0.66/1.04 inference(reduction,[status(thm)],['1.0.0.13','0.8.2.0',theory(equality)]),
% 0.66/1.04 [pos('R.2.2','L')]).
% 0.66/1.04 cnf('1.0.0.15',plain,
% 0.66/1.04 ( $true ),
% 0.66/1.04 inference(trivial,[status(thm)],['1.0.0.14',theory(equality)]),
% 0.66/1.04 [conjecture_1]).
% 0.66/1.04
% 0.66/1.04 Proved Goals:
% 0.66/1.04 No. 1: add(associator(u,x,y),associator(v,x,y)) ?= associator(add(u,v),x,y) joined, current: add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y)))) = add(additive_inverse(multiply(v,multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),multiply(multiply(u,x),y))))
% 0.66/1.04 1 goal was specified, which was proved.
% 0.66/1.04 % SZS output end CNFRefutation
% 0.66/1.04 #END OF PROOF
% 0.66/1.04
% 0.66/1.04 Problem WALDMEISTER_24309_n020
% 0.66/1.04 CPs.gen 492
% 0.66/1.04 CPs.reexp 0
% 0.66/1.04 Select 118
% 0.66/1.04 R 32
% 0.66/1.04 E 3
% 0.66/1.04 vsize 6.6M
% 0.66/1.04 rss 3.9M
% 0.66/1.04 process.time 0.005s
% 0.66/1.04 wallclock.time 0.005s
% 0.66/1.04 status S
% 0.66/1.04
% 0.66/1.04
% 0.66/1.04 Waldmeister states: Goal proved.
% 0.66/1.04 % SZS status Unsatisfiable
%------------------------------------------------------------------------------