TSTP Solution File: RNG021-7 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : RNG021-7 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:47:25 EDT 2022
% Result : Unsatisfiable 0.50s 0.89s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : RNG021-7 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.11 % Command : woody %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Mon May 30 15:08:12 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.50/0.89 ********************************************************************************
% 0.50/0.89 * W A L D M E I S T E R \| \ / \|/ *
% 0.50/0.89 * |/ | \/ | *
% 0.50/0.89 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.50/0.89 * A. Jaeger and B. Loechner | | *
% 0.50/0.89 * <waldmeister@informatik.uni-kl.de> | *
% 0.50/0.89 ********************************************************************************
% 0.50/0.89
% 0.50/0.89
% 0.50/0.89 Goals:
% 0.50/0.89 ------
% 0.50/0.89
% 0.50/0.89 ( 1) add(associator(u,x,y),associator(v,x,y)) ?=? associator(add(u,v),x,y)
% 0.50/0.89
% 0.50/0.89 Detected structure: NichtassoziativerRing
% 0.50/0.89 ********************************************************************************
% 0.50/0.89 ****************************** COMPLETION - PROOF ******************************
% 0.50/0.89 ********************************************************************************
% 0.50/0.89
% 0.50/0.89 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))))
% 0.50/0.89 goal joined
% 0.50/0.89 % SZS status Unsatisfiable
% 0.50/0.89 #START OF PROOF
% 0.50/0.89 % SZS output start CNFRefutation
% 0.50/0.89 cnf('0.2.0.0',axiom,
% 0.50/0.89 ( X1 = add(additive_identity,X1) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.2.1.0',plain,
% 0.50/0.89 ( X1 = add(additive_identity,X1) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.50/0.89 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.50/0.89 cnf('0.2.2.0',plain,
% 0.50/0.89 ( add(additive_identity,X1) = X1 ),
% 0.50/0.89 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.50/0.89 [x,rule_2]).
% 0.50/0.89 cnf('0.3.0.0',axiom,
% 0.50/0.89 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.3.1.0',plain,
% 0.50/0.89 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.50/0.89 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.50/0.89 cnf('0.3.2.0',plain,
% 0.50/0.89 ( additive_inverse(additive_inverse(X1)) = X1 ),
% 0.50/0.89 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.50/0.89 [x,rule_3]).
% 0.50/0.89 cnf('0.10.0.0',axiom,
% 0.50/0.89 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.10.1.0',plain,
% 0.50/0.89 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.50/0.89 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.50/0.89 cnf('0.10.2.0',plain,
% 0.50/0.89 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.50/0.89 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.50/0.89 [u,rule_10]).
% 0.50/0.89 cnf('0.14.0.0',axiom,
% 0.50/0.89 ( add(X1,X2) = add(X2,X1) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.14.1.0',plain,
% 0.50/0.89 ( add(X1,X2) = add(X2,X1) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.50/0.89 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.50/0.89 cnf('0.14.2.0',plain,
% 0.50/0.89 ( add(X1,X2) = add(X2,X1) ),
% 0.50/0.89 inference(activate,[status(thm)],['0.14.1.0']),
% 0.50/0.89 [equation_1]).
% 0.50/0.89 cnf('0.15.0.0',axiom,
% 0.50/0.89 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.15.1.0',plain,
% 0.50/0.89 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.50/0.89 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.50/0.89 cnf('0.15.2.0',plain,
% 0.50/0.89 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.50/0.89 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.50/0.89 [x,rule_14]).
% 0.50/0.89 cnf('0.16.0.0',axiom,
% 0.50/0.89 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.16.1.0',plain,
% 0.50/0.89 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.50/0.89 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.50/0.89 cnf('0.16.2.0',plain,
% 0.50/0.89 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.50/0.89 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.50/0.89 [u,rule_15]).
% 0.50/0.89 cnf('0.18.0.0',axiom,
% 0.50/0.89 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032')).
% 0.50/0.89 cnf('0.18.1.0',plain,
% 0.50/0.89 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.50/0.89 [weight('<20,0,0,[0,0,0,21]>')]).
% 0.50/0.89 cnf('0.18.1.1',plain,
% 0.50/0.89 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) = associator(X1,X2,X3) ),
% 0.50/0.89 inference(reduction,[status(thm)],['0.18.1.0','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('L','L')]).
% 0.50/0.89 cnf('0.18.2.0',plain,
% 0.50/0.89 ( associator(X1,X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) ),
% 0.50/0.89 inference(orient,[status(thm)],['0.18.1.1',theory(equality)]),
% 0.50/0.89 [x,rule_17]).
% 0.50/0.89 cnf('0.20.0.0',plain,
% 0.50/0.89 ( add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2) ),
% 0.50/0.89 inference(cp,[status(thm)],['0.15.2.0','0.16.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.1','L')]).
% 0.50/0.89 cnf('0.20.0.1',plain,
% 0.50/0.89 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.50/0.89 inference(reduction,[status(thm)],['0.20.0.0','0.2.2.0',theory(equality)]),
% 0.50/0.89 [pos('R','L')]).
% 0.50/0.89 cnf('0.20.1.0',plain,
% 0.50/0.89 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.20.0.1']),
% 0.50/0.89 [weight('<6,16,15,[0,0,0,1]>')]).
% 0.50/0.89 cnf('0.20.2.0',plain,
% 0.50/0.89 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.50/0.89 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.50/0.89 [u,rule_19]).
% 0.50/0.89 cnf('0.21.0.0',plain,
% 0.50/0.89 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.50/0.89 inference(cp,[status(thm)],['0.20.2.0','0.3.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.2.1','L')]).
% 0.50/0.89 cnf('0.21.1.0',plain,
% 0.50/0.89 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.50/0.89 [weight('<6,20,3,[1,0,0,3]>')]).
% 0.50/0.89 cnf('0.21.2.0',plain,
% 0.50/0.89 ( add(additive_inverse(X1),add(X1,X2)) = X2 ),
% 0.50/0.89 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.50/0.89 [x,rule_20]).
% 0.50/0.89 cnf('0.23.0.0',plain,
% 0.50/0.89 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.50/0.89 inference(cp,[status(thm)],['0.21.2.0','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.2','L')]).
% 0.50/0.89 cnf('0.23.1.0',plain,
% 0.50/0.89 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.50/0.89 [weight('<6,21,14,[1,0,0,3]>')]).
% 0.50/0.89 cnf('0.23.2.0',plain,
% 0.50/0.89 ( add(additive_inverse(X1),add(X2,X1)) = X2 ),
% 0.50/0.89 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.50/0.89 [x,rule_22]).
% 0.50/0.89 cnf('0.24.0.0',plain,
% 0.50/0.89 ( additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2) ),
% 0.50/0.89 inference(cp,[status(thm)],['0.23.2.0','0.21.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.2','L')]).
% 0.50/0.89 cnf('0.24.1.0',plain,
% 0.50/0.89 ( additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.50/0.89 [weight('<6,23,21,[1,0,0,3]>')]).
% 0.50/0.89 cnf('0.24.1.1',plain,
% 0.50/0.89 ( additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))) ),
% 0.50/0.89 inference(reduction,[status(thm)],['0.24.1.0','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('R','L')]).
% 0.50/0.89 cnf('0.24.2.0',plain,
% 0.50/0.89 ( add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2) ),
% 0.50/0.89 inference(orient,[status(thm)],['0.24.1.1',theory(equality)]),
% 0.50/0.89 [x,rule_23]).
% 0.50/0.89 cnf('0.25.0.0',plain,
% 0.50/0.89 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.50/0.89 inference(cp,[status(thm)],['0.21.2.0','0.24.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.2','L')]).
% 0.50/0.89 cnf('0.25.1.0',plain,
% 0.50/0.89 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.50/0.89 [weight('<4,24,21,[0,0,0,3]>')]).
% 0.50/0.89 cnf('0.25.2.0',plain,
% 0.50/0.89 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.50/0.89 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.50/0.89 [u,rule_24]).
% 0.50/0.89 cnf('0.33.0.0',plain,
% 0.50/0.89 ( add(X1,add(X2,X3)) = add(add(X2,X1),X3) ),
% 0.50/0.89 inference(cp,[status(thm)],['0.15.2.0','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.1','L')]).
% 0.50/0.89 cnf('0.33.0.1',plain,
% 0.50/0.89 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.50/0.89 inference(reduction,[status(thm)],['0.33.0.0','0.15.2.0',theory(equality)]),
% 0.50/0.89 [pos('R','L')]).
% 0.50/0.89 cnf('0.33.1.0',plain,
% 0.50/0.89 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.50/0.89 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.50/0.89 [weight('<10,15,14,[1,0,0,1]>')]).
% 0.50/0.89 cnf('0.33.2.0',plain,
% 0.50/0.89 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.50/0.89 inference(activate,[status(thm)],['0.33.1.0']),
% 0.50/0.89 [equation_3]).
% 0.50/0.89 cnf('1.0.0.0',conjecture,
% 0.50/0.89 ( add(associator(u,x,y),associator(v,x,y)) = associator(add(u,v),x,y) ),
% 0.50/0.89 file('/tmp/WALDMEISTER_26680_n032',conjecture_1)).
% 0.50/0.89 cnf('1.0.0.1',plain,
% 0.50/0.89 ( add(associator(v,x,y),associator(u,x,y)) = associator(add(u,v),x,y) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.0','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('L','L')]).
% 0.50/0.89 cnf('1.0.0.2',plain,
% 0.50/0.89 ( add(add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y)),associator(u,x,y)) = associator(add(u,v),x,y) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.1','0.18.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.1','L')]).
% 0.50/0.89 cnf('1.0.0.3',plain,
% 0.50/0.89 ( add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(v,x),y),associator(u,x,y))) = associator(add(u,v),x,y) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.2','0.15.2.0',theory(equality)]),
% 0.50/0.89 [pos('L','L')]).
% 0.50/0.89 cnf('1.0.0.4',plain,
% 0.50/0.89 ( 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) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.3','0.18.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.2.2','L')]).
% 0.50/0.89 cnf('1.0.0.5',plain,
% 0.50/0.89 ( 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) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.4','0.33.2.0',theory(equality)]),
% 0.50/0.89 [pos('L.2','L')]).
% 0.50/0.89 cnf('1.0.0.6',plain,
% 0.50/0.89 ( 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)) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.5','0.18.2.0',theory(equality)]),
% 0.50/0.89 [pos('R','L')]).
% 0.50/0.89 cnf('1.0.0.7',plain,
% 0.50/0.89 ( 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)) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.6','0.10.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.1.1','L')]).
% 0.50/0.89 cnf('1.0.0.8',plain,
% 0.50/0.89 ( 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)) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.7','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.1.1','L')]).
% 0.50/0.89 cnf('1.0.0.9',plain,
% 0.50/0.89 ( 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)) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.8','0.25.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.1','L')]).
% 0.50/0.89 cnf('1.0.0.10',plain,
% 0.50/0.89 ( 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)) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.9','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.1','L')]).
% 0.50/0.89 cnf('1.0.0.11',plain,
% 0.50/0.89 ( 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))) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.10','0.15.2.0',theory(equality)]),
% 0.50/0.89 [pos('R','L')]).
% 0.50/0.89 cnf('1.0.0.12',plain,
% 0.50/0.89 ( 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))) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.11','0.10.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.2.2.1','L')]).
% 0.50/0.89 cnf('1.0.0.13',plain,
% 0.50/0.89 ( 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))) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.12','0.14.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.2.2.1','L')]).
% 0.50/0.89 cnf('1.0.0.14',plain,
% 0.50/0.89 ( 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)))) ),
% 0.50/0.89 inference(reduction,[status(thm)],['1.0.0.13','0.10.2.0',theory(equality)]),
% 0.50/0.89 [pos('R.2.2','L')]).
% 0.50/0.89 cnf('1.0.0.15',plain,
% 0.50/0.89 ( $true ),
% 0.50/0.89 inference(trivial,[status(thm)],['1.0.0.14',theory(equality)]),
% 0.50/0.89 [conjecture_1]).
% 0.50/0.89
% 0.50/0.89 Proved Goals:
% 0.50/0.89 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))))
% 0.50/0.89 1 goal was specified, which was proved.
% 0.50/0.89 % SZS output end CNFRefutation
% 0.50/0.89 #END OF PROOF
% 0.50/0.89
% 0.50/0.89 Problem WALDMEISTER_26680_n032
% 0.50/0.89 CPs.gen 440
% 0.50/0.89 CPs.reexp 0
% 0.50/0.89 Select 124
% 0.50/0.89 R 30
% 0.50/0.89 E 3
% 0.50/0.89 vsize 6.6M
% 0.50/0.89 rss 3.9M
% 0.50/0.89 process.time 0.004s
% 0.50/0.89 wallclock.time 0.004s
% 0.50/0.89 status S
% 0.50/0.89
% 0.50/0.89
% 0.50/0.89 Waldmeister states: Goal proved.
% 0.50/0.89 % SZS status Unsatisfiable
%------------------------------------------------------------------------------