TSTP Solution File: RNG025-4 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : RNG025-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n023.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 20:47:26 EDT 2022
% Result : Unsatisfiable 0.63s 1.17s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 21:19:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.60/1.01 ********************************************************************************
% 0.60/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/1.01 * |/ | \/ | *
% 0.60/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/1.01 * A. Jaeger and B. Loechner | | *
% 0.60/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/1.01 ********************************************************************************
% 0.60/1.01
% 0.60/1.01
% 0.60/1.01 Goals:
% 0.60/1.01 ------
% 0.60/1.01
% 0.60/1.01 ( 1) add(associator(x,y,z),associator(x,z,y)) ?=? additive_identity
% 0.60/1.01
% 0.60/1.01 Detected structure: NichtassoziativerRing
% 0.60/1.01 ********************************************************************************
% 0.60/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.60/1.01 ********************************************************************************
% 0.60/1.01
% 0.63/1.17 joined goal: 1 add(associator(x,y,z),associator(x,z,y)) ?= additive_identity to additive_identity
% 0.63/1.17 goal joined
% 0.63/1.17 % SZS status Unsatisfiable
% 0.63/1.17 #START OF PROOF
% 0.63/1.17 % SZS output start CNFRefutation
% 0.63/1.17 cnf('0.1.0.0',axiom,
% 0.63/1.17 ( X1 = add(X1,additive_identity) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.1.1.0',plain,
% 0.63/1.17 ( X1 = add(X1,additive_identity) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.63/1.17 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.63/1.17 cnf('0.1.2.0',plain,
% 0.63/1.17 ( add(X1,additive_identity) = X1 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_1]).
% 0.63/1.17 cnf('0.2.0.0',axiom,
% 0.63/1.17 ( X1 = add(additive_identity,X1) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.2.1.0',plain,
% 0.63/1.17 ( X1 = add(additive_identity,X1) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.63/1.17 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.63/1.17 cnf('0.2.2.0',plain,
% 0.63/1.17 ( add(additive_identity,X1) = X1 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_2]).
% 0.63/1.17 cnf('0.3.0.0',axiom,
% 0.63/1.17 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.3.1.0',plain,
% 0.63/1.17 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.63/1.17 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.63/1.17 cnf('0.3.2.0',plain,
% 0.63/1.17 ( additive_inverse(additive_inverse(X1)) = X1 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_3]).
% 0.63/1.17 cnf('0.4.0.0',axiom,
% 0.63/1.17 ( multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.4.1.0',plain,
% 0.63/1.17 ( multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.63/1.17 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.63/1.17 cnf('0.4.2.0',plain,
% 0.63/1.17 ( multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_4]).
% 0.63/1.17 cnf('0.5.0.0',axiom,
% 0.63/1.17 ( multiply(X1,multiply(X1,X2)) = multiply(multiply(X1,X1),X2) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.5.1.0',plain,
% 0.63/1.17 ( multiply(X1,multiply(X1,X2)) = multiply(multiply(X1,X1),X2) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.63/1.17 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.63/1.17 cnf('0.5.2.0',plain,
% 0.63/1.17 ( multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_5]).
% 0.63/1.17 cnf('0.6.0.0',axiom,
% 0.63/1.17 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.6.1.0',plain,
% 0.63/1.17 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.63/1.17 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.63/1.17 cnf('0.6.2.0',plain,
% 0.63/1.17 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_6]).
% 0.63/1.17 cnf('0.8.0.0',axiom,
% 0.63/1.17 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.8.1.0',plain,
% 0.63/1.17 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.63/1.17 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.63/1.17 cnf('0.8.2.0',plain,
% 0.63/1.17 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_8]).
% 0.63/1.17 cnf('0.10.0.0',axiom,
% 0.63/1.17 ( add(X1,X2) = add(X2,X1) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.10.1.0',plain,
% 0.63/1.17 ( add(X1,X2) = add(X2,X1) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.63/1.17 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.63/1.17 cnf('0.10.2.0',plain,
% 0.63/1.17 ( add(X1,X2) = add(X2,X1) ),
% 0.63/1.17 inference(activate,[status(thm)],['0.10.1.0']),
% 0.63/1.17 [equation_1]).
% 0.63/1.17 cnf('0.11.0.0',axiom,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.11.1.0',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.63/1.17 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.63/1.17 cnf('0.11.2.0',plain,
% 0.63/1.17 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_10]).
% 0.63/1.17 cnf('0.12.0.0',axiom,
% 0.63/1.17 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.12.1.0',plain,
% 0.63/1.17 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.63/1.17 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.63/1.17 cnf('0.12.2.0',plain,
% 0.63/1.17 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.63/1.17 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_11]).
% 0.63/1.17 cnf('0.14.0.0',axiom,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023')).
% 0.63/1.17 cnf('0.14.1.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.63/1.17 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.63/1.17 cnf('0.14.1.1',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) = associator(X1,X2,X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.14.1.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.14.2.0',plain,
% 0.63/1.17 ( associator(X1,X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 0.63/1.17 [x,rule_13]).
% 0.63/1.17 cnf('0.16.0.0',plain,
% 0.63/1.17 ( add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.11.2.0','0.12.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.16.0.1',plain,
% 0.63/1.17 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.16.0.0','0.2.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.16.1.0',plain,
% 0.63/1.17 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.16.0.1']),
% 0.63/1.17 [weight('<6,12,11,[0,0,0,1]>')]).
% 0.63/1.17 cnf('0.16.2.0',plain,
% 0.63/1.17 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_15]).
% 0.63/1.17 cnf('0.17.0.0',plain,
% 0.63/1.17 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.1','L')]).
% 0.63/1.17 cnf('0.17.1.0',plain,
% 0.63/1.17 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.63/1.17 [weight('<6,16,3,[1,0,0,3]>')]).
% 0.63/1.17 cnf('0.17.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X1,X2)) = X2 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_16]).
% 0.63/1.17 cnf('0.18.0.0',plain,
% 0.63/1.17 ( X1 = add(X2,add(X1,additive_inverse(X2))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.16.2.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.18.1.0',plain,
% 0.63/1.17 ( X1 = add(X2,add(X1,additive_inverse(X2))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.63/1.17 [weight('<6,16,10,[1,0,0,2]>')]).
% 0.63/1.17 cnf('0.18.2.0',plain,
% 0.63/1.17 ( add(X1,add(X2,additive_inverse(X1))) = X2 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_17]).
% 0.63/1.17 cnf('0.19.0.0',plain,
% 0.63/1.17 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.17.2.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.19.1.0',plain,
% 0.63/1.17 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.63/1.17 [weight('<6,17,10,[1,0,0,3]>')]).
% 0.63/1.17 cnf('0.19.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,X1)) = X2 ),
% 0.63/1.17 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_18]).
% 0.63/1.17 cnf('0.20.0.0',plain,
% 0.63/1.17 ( additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.19.2.0','0.17.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.20.1.0',plain,
% 0.63/1.17 ( additive_inverse(X1) = add(additive_inverse(add(X1,X2)),X2) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.63/1.17 [weight('<6,19,17,[1,0,0,3]>')]).
% 0.63/1.17 cnf('0.20.1.1',plain,
% 0.63/1.17 ( additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.20.1.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.20.2.0',plain,
% 0.63/1.17 ( add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.20.1.1',theory(equality)]),
% 0.63/1.17 [x,rule_19]).
% 0.63/1.17 cnf('0.21.0.0',plain,
% 0.63/1.17 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.17.2.0','0.20.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.21.1.0',plain,
% 0.63/1.17 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.63/1.17 [weight('<4,20,17,[0,0,0,3]>')]).
% 0.63/1.17 cnf('0.21.2.0',plain,
% 0.63/1.17 ( additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_20]).
% 0.63/1.17 cnf('0.32.0.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(add(X2,X1),X3)) = add(X2,X3) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.11.2.0','0.19.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.32.0.1',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.32.0.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.32.1.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.32.0.1']),
% 0.63/1.17 [weight('<8,19,11,[0,0,0,1]>')]).
% 0.63/1.17 cnf('0.32.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_31]).
% 0.63/1.17 cnf('0.33.0.0',plain,
% 0.63/1.17 ( add(X1,X2) = add(additive_inverse(X3),add(X1,add(X2,X3))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.19.2.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.33.1.0',plain,
% 0.63/1.17 ( add(X1,X2) = add(additive_inverse(X3),add(X1,add(X2,X3))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.33.0.0']),
% 0.63/1.17 [weight('<8,19,11,[1,0,0,3]>')]).
% 0.63/1.17 cnf('0.33.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,add(X3,X1))) = add(X2,X3) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_32]).
% 0.63/1.17 cnf('0.35.0.0',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(add(X2,X1),X3) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.11.2.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.35.0.1',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.35.0.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.35.1.0',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.35.0.1']),
% 0.63/1.17 [weight('<10,11,10,[1,0,0,1]>')]).
% 0.63/1.17 cnf('0.35.2.0',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.63/1.17 inference(activate,[status(thm)],['0.35.1.0']),
% 0.63/1.17 [equation_3]).
% 0.63/1.17 cnf('0.38.0.0',plain,
% 0.63/1.17 ( add(add(X1,X2),X3) = add(additive_inverse(X4),add(X1,add(X2,add(X4,X3)))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.32.2.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.38.0.1',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X4,X3)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.38.0.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.38.1.0',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X4,X3)))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.38.0.1']),
% 0.63/1.17 [weight('<10,32,11,[1,0,0,3]>')]).
% 0.63/1.17 cnf('0.38.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,add(X3,add(X1,X4)))) = add(X2,add(X3,X4)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_35]).
% 0.63/1.17 cnf('0.39.0.0',plain,
% 0.63/1.17 ( add(add(X1,X2),X3) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.33.2.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.39.0.1',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.39.0.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.39.1.0',plain,
% 0.63/1.17 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.39.0.1']),
% 0.63/1.17 [weight('<10,33,11,[1,0,0,3]>')]).
% 0.63/1.17 cnf('0.39.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(X1),add(X2,add(X3,add(X4,X1)))) = add(X2,add(X3,X4)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_36]).
% 0.63/1.17 cnf('0.41.0.0',plain,
% 0.63/1.17 ( multiply(add(X1,X2),multiply(add(X1,X2),X3)) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.5.2.0','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.41.1.0',plain,
% 0.63/1.17 ( multiply(add(X1,X2),multiply(add(X1,X2),X3)) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.41.0.0']),
% 0.63/1.17 [weight('<13,6,5,[0,0,0,1]>')]).
% 0.63/1.17 cnf('0.41.1.1',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(add(X1,X2),X3)),multiply(X2,multiply(add(X1,X2),X3))) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.0','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.41.1.2',plain,
% 0.63/1.17 ( add(multiply(X1,add(multiply(X1,X3),multiply(X2,X3))),multiply(X2,multiply(add(X1,X2),X3))) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.1','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1.2','L')]).
% 0.63/1.17 cnf('0.41.1.3',plain,
% 0.63/1.17 ( add(add(multiply(X1,multiply(X1,X3)),multiply(X1,multiply(X2,X3))),multiply(X2,multiply(add(X1,X2),X3))) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.2','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.41.1.4',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),multiply(X2,multiply(add(X1,X2),X3)))) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.3','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.41.1.5',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),multiply(X2,add(multiply(X1,X3),multiply(X2,X3))))) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.4','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2.2','L')]).
% 0.63/1.17 cnf('0.41.1.6',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.5','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('0.41.1.7',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(multiply(add(X1,X2),X1),X3),multiply(multiply(add(X1,X2),X2),X3)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.6','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.41.1.8',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(add(multiply(X1,X1),multiply(X2,X1)),X3),multiply(multiply(add(X1,X2),X2),X3)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.7','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.1.1','L')]).
% 0.63/1.17 cnf('0.41.1.9',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(add(multiply(multiply(X1,X1),X3),multiply(multiply(X2,X1),X3)),multiply(multiply(add(X1,X2),X2),X3)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.8','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.1','L')]).
% 0.63/1.17 cnf('0.41.1.10',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(multiply(X1,X1),X3),add(multiply(multiply(X2,X1),X3),multiply(multiply(add(X1,X2),X2),X3))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.9','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.41.1.11',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(X1,multiply(X1,X3)),add(multiply(multiply(X2,X1),X3),multiply(multiply(add(X1,X2),X2),X3))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.10','0.5.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.1','L')]).
% 0.63/1.17 cnf('0.41.1.12',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(X1,multiply(X1,X3)),add(multiply(multiply(X2,X1),X3),multiply(add(multiply(X1,X2),multiply(X2,X2)),X3))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.11','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2.2.1','L')]).
% 0.63/1.17 cnf('0.41.1.13',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(X1,multiply(X1,X3)),add(multiply(multiply(X2,X1),X3),add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X2),X3)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.12','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2.2','L')]).
% 0.63/1.17 cnf('0.41.1.14',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(X1,multiply(X1,X3)),add(multiply(multiply(X2,X1),X3),add(multiply(multiply(X1,X2),X3),multiply(X2,multiply(X2,X3))))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.13','0.5.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2.2.2','L')]).
% 0.63/1.17 cnf('0.41.1.15',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(X1,multiply(X1,X3)),add(multiply(multiply(X2,X1),X3),add(multiply(X2,multiply(X2,X3)),multiply(multiply(X1,X2),X3)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.14','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2.2','L')]).
% 0.63/1.17 cnf('0.41.1.16',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X3)),add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3))))) = add(multiply(X1,multiply(X1,X3)),add(multiply(X2,multiply(X2,X3)),add(multiply(multiply(X2,X1),X3),multiply(multiply(X1,X2),X3)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.41.1.15','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2','L')]).
% 0.63/1.17 cnf('0.41.2.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X2)),add(multiply(multiply(X1,X3),X2),multiply(multiply(X3,X1),X2))) = add(multiply(X3,multiply(X1,X2)),add(multiply(X1,multiply(X3,X2)),multiply(X1,multiply(X1,X2)))) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.41.1.16',theory(equality)]),
% 0.63/1.17 [x,rule_37]).
% 0.63/1.17 cnf('0.42.0.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3)))) = add(multiply(X2,multiply(X2,X3)),add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.41.2.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.42.1.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),multiply(X2,multiply(X2,X3)))) = add(multiply(X2,multiply(X2,X3)),add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.63/1.17 [weight('<17,41,0,[1,0,0,6]>')]).
% 0.63/1.17 cnf('0.42.2.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X1,X2)),add(multiply(multiply(X3,X1),X2),multiply(multiply(X1,X3),X2))) = add(multiply(X3,multiply(X1,X2)),add(multiply(X1,multiply(X3,X2)),multiply(X1,multiply(X1,X2)))) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_38]).
% 0.63/1.17 cnf('0.43.0.0',plain,
% 0.63/1.17 ( add(X1,add(multiply(multiply(X2,X3),X4),multiply(multiply(X3,X2),X4))) = add(additive_inverse(multiply(X3,multiply(X3,X4))),add(X1,add(multiply(X2,multiply(X3,X4)),add(multiply(X3,multiply(X2,X4)),multiply(X3,multiply(X3,X4)))))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.32.2.0','0.42.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('0.43.0.1',plain,
% 0.63/1.17 ( add(X1,add(multiply(multiply(X2,X3),X4),multiply(multiply(X3,X2),X4))) = add(X1,add(multiply(X2,multiply(X3,X4)),multiply(X3,multiply(X2,X4)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.43.0.0','0.39.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.43.1.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X2,X3),X4),multiply(multiply(X3,X2),X4)) = add(multiply(X2,multiply(X3,X4)),multiply(X3,multiply(X2,X4))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.43.0.1']),
% 0.63/1.17 [weight('<11,42,32,[0,0,0,5]>')]).
% 0.63/1.17 cnf('0.43.2.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3)) = add(multiply(X1,multiply(X2,X3)),multiply(X2,multiply(X1,X3))) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_39]).
% 0.63/1.17 cnf('0.44.0.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X2)),multiply(X2,multiply(X1,X2))) = add(multiply(X1,multiply(X2,X2)),multiply(multiply(X2,X1),X2)) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.43.2.0','0.4.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.44.1.0',plain,
% 0.63/1.17 ( multiply(X2,multiply(X1,X2)) = multiply(multiply(X2,X1),X2) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.44.0.0']),
% 0.63/1.17 [weight('<5,43,4,[1,0,0,1]>')]).
% 0.63/1.17 cnf('0.44.2.0',plain,
% 0.63/1.17 ( multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 0.63/1.17 [x,rule_40]).
% 0.63/1.17 cnf('0.49.0.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),add(multiply(multiply(X2,X1),X3),X4)) = add(add(multiply(X1,multiply(X2,X3)),multiply(X2,multiply(X1,X3))),X4) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.11.2.0','0.43.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.49.0.1',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),add(multiply(multiply(X2,X1),X3),X4)) = add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),X4)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.49.0.0','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.49.1.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),add(multiply(multiply(X2,X1),X3),X4)) = add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),X4)) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.49.0.1']),
% 0.63/1.17 [weight('<13,43,11,[0,0,0,1]>')]).
% 0.63/1.17 cnf('0.49.2.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),add(multiply(multiply(X2,X1),X3),X4)) = add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),X4)) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_45]).
% 0.63/1.17 cnf('0.63.0.0',plain,
% 0.63/1.17 ( multiply(add(X1,X2),multiply(X3,add(X1,X2))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.44.2.0','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.63.0.1',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,add(X1,X2))),multiply(X2,multiply(X3,add(X1,X2)))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.0','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.63.0.2',plain,
% 0.63/1.17 ( add(multiply(X1,add(multiply(X3,X1),multiply(X3,X2))),multiply(X2,multiply(X3,add(X1,X2)))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.1','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1.2','L')]).
% 0.63/1.17 cnf('0.63.0.3',plain,
% 0.63/1.17 ( add(add(multiply(X1,multiply(X3,X1)),multiply(X1,multiply(X3,X2))),multiply(X2,multiply(X3,add(X1,X2)))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.2','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.63.0.4',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),multiply(X2,multiply(X3,add(X1,X2))))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.3','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('0.63.0.5',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),multiply(X2,add(multiply(X3,X1),multiply(X3,X2))))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.4','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2.2','L')]).
% 0.63/1.17 cnf('0.63.0.6',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.5','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('0.63.0.7',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = add(multiply(multiply(X1,X3),add(X1,X2)),multiply(multiply(X2,X3),add(X1,X2))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.6','0.8.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.63.0.8',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = add(add(multiply(multiply(X1,X3),X1),multiply(multiply(X1,X3),X2)),multiply(multiply(X2,X3),add(X1,X2))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.7','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.1','L')]).
% 0.63/1.17 cnf('0.63.0.9',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = add(multiply(multiply(X1,X3),X1),add(multiply(multiply(X1,X3),X2),multiply(multiply(X2,X3),add(X1,X2)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.8','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.63.0.10',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = add(multiply(X1,multiply(X3,X1)),add(multiply(multiply(X1,X3),X2),multiply(multiply(X2,X3),add(X1,X2)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.9','0.44.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.1','L')]).
% 0.63/1.17 cnf('0.63.0.11',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = add(multiply(X1,multiply(X3,X1)),add(multiply(multiply(X1,X3),X2),add(multiply(multiply(X2,X3),X1),multiply(multiply(X2,X3),X2)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.10','0.6.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2.2','L')]).
% 0.63/1.17 cnf('0.63.0.12',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X1)),add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2))))) = add(multiply(X1,multiply(X3,X1)),add(multiply(multiply(X1,X3),X2),add(multiply(multiply(X2,X3),X1),multiply(X2,multiply(X3,X2))))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.0.11','0.44.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2.2.2','L')]).
% 0.63/1.17 cnf('0.63.1.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2)))) = add(multiply(multiply(X1,X3),X2),add(multiply(multiply(X2,X3),X1),multiply(X2,multiply(X3,X2)))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.63.0.12']),
% 0.63/1.17 [weight('<17,44,8,[1,0,0,1]>')]).
% 0.63/1.17 cnf('0.63.1.1',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X3,X2)),add(multiply(X2,multiply(X3,X1)),multiply(X2,multiply(X3,X2)))) = add(multiply(multiply(X1,X3),X2),add(multiply(X2,multiply(X3,X2)),multiply(multiply(X2,X3),X1))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.63.1.0','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('R.2','L')]).
% 0.63/1.17 cnf('0.63.2.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),add(multiply(X3,multiply(X2,X3)),multiply(multiply(X3,X2),X1))) = add(multiply(X1,multiply(X2,X3)),add(multiply(X3,multiply(X2,X1)),multiply(X3,multiply(X2,X3)))) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.63.1.1',theory(equality)]),
% 0.63/1.17 [x,rule_59]).
% 0.63/1.17 cnf('0.64.0.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(additive_inverse(multiply(X3,multiply(X2,X3))),add(multiply(X1,multiply(X2,X3)),add(multiply(X3,multiply(X2,X1)),multiply(X3,multiply(X2,X3))))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.32.2.0','0.63.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.64.0.1',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X2,X1))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.64.0.0','0.33.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.64.1.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X2,X1))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.64.0.1']),
% 0.63/1.17 [weight('<11,63,32,[0,0,0,3]>')]).
% 0.63/1.17 cnf('0.64.2.0',plain,
% 0.63/1.17 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X2,X1))) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_60]).
% 0.63/1.17 cnf('0.70.0.0',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(multiply(X1,X2),X3)),additive_inverse(multiply(multiply(X3,X2),X1))) = additive_inverse(add(multiply(X3,multiply(X2,X1)),multiply(X1,multiply(X2,X3)))) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.21.2.0','0.64.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('0.70.0.1',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(multiply(X1,X2),X3)),additive_inverse(multiply(multiply(X3,X2),X1))) = add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.70.0.0','0.21.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.70.1.0',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(multiply(X1,X2),X3)),additive_inverse(multiply(multiply(X3,X2),X1))) = add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.70.0.1']),
% 0.63/1.17 [weight('<13,64,21,[0,0,0,1]>')]).
% 0.63/1.17 cnf('0.70.2.0',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(multiply(X1,X2),X3)),additive_inverse(multiply(multiply(X3,X2),X1))) = add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) ),
% 0.63/1.17 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 0.63/1.17 [u,rule_66]).
% 0.63/1.17 cnf('0.152.0.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = add(multiply(multiply(X1,X2),X3),additive_identity) ),
% 0.63/1.17 inference(cp,[status(thm)],['0.49.2.0','0.12.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('0.152.0.1',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = multiply(multiply(X1,X2),X3) ),
% 0.63/1.17 inference(reduction,[status(thm)],['0.152.0.0','0.1.2.0',theory(equality)]),
% 0.63/1.17 [pos('R','L')]).
% 0.63/1.17 cnf('0.152.1.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = multiply(multiply(X1,X2),X3) ),
% 0.63/1.17 inference(weigh,[status(thm)],['0.152.0.1']),
% 0.63/1.17 [weight('<23,49,12,[1,0,0,6]>')]).
% 0.63/1.17 cnf('0.152.2.0',plain,
% 0.63/1.17 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = multiply(multiply(X1,X2),X3) ),
% 0.63/1.17 inference(activate,[status(thm)],['0.152.1.0']),
% 0.63/1.17 [equation_6]).
% 0.63/1.17 cnf('1.0.0.0',conjecture,
% 0.63/1.17 ( add(associator(x,y,z),associator(x,z,y)) = additive_identity ),
% 0.63/1.17 file('/tmp/WALDMEISTER_3029_n023',conjecture_1)).
% 0.63/1.17 cnf('1.0.0.1',plain,
% 0.63/1.17 ( add(add(additive_inverse(multiply(x,multiply(y,z))),multiply(multiply(x,y),z)),associator(x,z,y)) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.0','0.14.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.1','L')]).
% 0.63/1.17 cnf('1.0.0.2',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(multiply(x,y),z),associator(x,z,y))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.1','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('1.0.0.3',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(x,multiply(y,z))),add(add(multiply(x,multiply(y,z)),add(multiply(y,multiply(x,z)),additive_inverse(multiply(multiply(y,x),z)))),associator(x,z,y))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.2','0.152.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.1','R')]).
% 0.63/1.17 cnf('1.0.0.4',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(x,multiply(y,z))),add(add(multiply(y,multiply(x,z)),add(multiply(x,multiply(y,z)),additive_inverse(multiply(multiply(y,x),z)))),associator(x,z,y))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.3','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.1','L')]).
% 0.63/1.17 cnf('1.0.0.5',plain,
% 0.63/1.17 ( add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(y,multiply(x,z)),add(add(multiply(x,multiply(y,z)),additive_inverse(multiply(multiply(y,x),z))),associator(x,z,y)))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.4','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('1.0.0.6',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(x,multiply(y,z))),add(add(multiply(x,multiply(y,z)),additive_inverse(multiply(multiply(y,x),z))),associator(x,z,y)))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.5','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('1.0.0.7',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(x,multiply(y,z)),add(additive_inverse(multiply(multiply(y,x),z)),associator(x,z,y))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.6','0.11.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('1.0.0.8',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(multiply(x,multiply(y,z)),add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(multiply(y,x),z)),associator(x,z,y))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.7','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('1.0.0.9',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(multiply(y,x),z)),associator(x,z,y))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.8','0.16.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('1.0.0.10',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(multiply(y,x),z)),add(additive_inverse(multiply(x,multiply(z,y))),multiply(multiply(x,z),y)))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.9','0.14.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('1.0.0.11',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(x,multiply(z,y))),add(additive_inverse(multiply(multiply(y,x),z)),multiply(multiply(x,z),y)))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.10','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('1.0.0.12',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(x,multiply(z,y))),add(additive_inverse(multiply(multiply(y,x),z)),add(multiply(x,multiply(z,y)),add(multiply(z,multiply(x,y)),additive_inverse(multiply(multiply(z,x),y))))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.11','0.152.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2.2','R')]).
% 0.63/1.17 cnf('1.0.0.13',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(x,multiply(z,y))),add(additive_inverse(multiply(multiply(y,x),z)),add(multiply(z,multiply(x,y)),add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(z,x),y))))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.12','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2.2','L')]).
% 0.63/1.17 cnf('1.0.0.14',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(z,multiply(x,y)),add(additive_inverse(multiply(multiply(y,x),z)),add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(z,x),y))))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.13','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('1.0.0.15',plain,
% 0.63/1.17 ( add(multiply(y,multiply(x,z)),add(multiply(z,multiply(x,y)),add(additive_inverse(multiply(multiply(y,x),z)),additive_inverse(multiply(multiply(z,x),y))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.14','0.38.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2','L')]).
% 0.63/1.17 cnf('1.0.0.16',plain,
% 0.63/1.17 ( add(multiply(z,multiply(x,y)),add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(multiply(y,x),z)),additive_inverse(multiply(multiply(z,x),y))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.15','0.35.2.0',theory(equality)]),
% 0.63/1.17 [pos('L','L')]).
% 0.63/1.17 cnf('1.0.0.17',plain,
% 0.63/1.17 ( add(multiply(z,multiply(x,y)),add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(y,multiply(x,z))),additive_inverse(multiply(z,multiply(x,y)))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.16','0.70.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('1.0.0.18',plain,
% 0.63/1.17 ( add(multiply(z,multiply(x,y)),add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(z,multiply(x,y))),additive_inverse(multiply(y,multiply(x,z)))))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.17','0.10.2.0',theory(equality)]),
% 0.63/1.17 [pos('L.2.2','L')]).
% 0.63/1.17 cnf('1.0.0.19',plain,
% 0.63/1.17 ( add(multiply(z,multiply(x,y)),additive_inverse(multiply(z,multiply(x,y)))) = additive_identity ),
% 0.63/1.17 inference(reduction,[status(thm)],['1.0.0.18','0.18.2.0',theory(equality)]),
% 0.63/1.18 [pos('L.2','L')]).
% 0.63/1.18 cnf('1.0.0.20',plain,
% 0.63/1.18 ( additive_identity = additive_identity ),
% 0.63/1.18 inference(reduction,[status(thm)],['1.0.0.19','0.12.2.0',theory(equality)]),
% 0.63/1.18 [pos('L','L')]).
% 0.63/1.18 cnf('1.0.0.21',plain,
% 0.63/1.18 ( $true ),
% 0.63/1.18 inference(trivial,[status(thm)],['1.0.0.20',theory(equality)]),
% 0.63/1.18 [conjecture_1]).
% 0.63/1.18
% 0.63/1.18 Proved Goals:
% 0.63/1.18 No. 1: add(associator(x,y,z),associator(x,z,y)) ?= additive_identity joined, current: additive_identity = additive_identity
% 0.63/1.18 1 goal was specified, which was proved.
% 0.63/1.18 % SZS output end CNFRefutation
% 0.63/1.18 #END OF PROOF
% 0.63/1.18
% 0.63/1.18 Problem WALDMEISTER_3029_n023
% 0.63/1.18 CPs.gen 11292
% 0.63/1.18 CPs.reexp 0
% 0.63/1.18 Select 869
% 0.63/1.18 R 146
% 0.63/1.18 E 6
% 0.63/1.18 vsize 6.7M
% 0.63/1.18 rss 3.9M
% 0.63/1.18 process.time 0.164s
% 0.63/1.18 wallclock.time 0.164s
% 0.63/1.18 status S
% 0.63/1.18
% 0.63/1.18
% 0.63/1.18 Waldmeister states: Goal proved.
% 0.63/1.18 % SZS status Unsatisfiable
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