TSTP Solution File: RNG025-7 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : RNG025-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n019.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 0.61s 1.02s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG025-7 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : woody %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 06:17:55 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.61/1.02 ********************************************************************************
% 0.61/1.02 * W A L D M E I S T E R \| \ / \|/ *
% 0.61/1.02 * |/ | \/ | *
% 0.61/1.02 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.61/1.02 * A. Jaeger and B. Loechner | | *
% 0.61/1.02 * <waldmeister@informatik.uni-kl.de> | *
% 0.61/1.02 ********************************************************************************
% 0.61/1.02
% 0.61/1.02
% 0.61/1.02 Goals:
% 0.61/1.02 ------
% 0.61/1.02
% 0.61/1.02 ( 1) additive_identity ?=? associator(x,y,x)
% 0.61/1.02
% 0.61/1.02 Detected structure: NichtassoziativerRing
% 0.61/1.02 ********************************************************************************
% 0.61/1.02 ****************************** COMPLETION - PROOF ******************************
% 0.61/1.02 ********************************************************************************
% 0.61/1.02
% 0.61/1.02 joined goal: 1 additive_identity ?= associator(x,y,x) to additive_identity
% 0.61/1.02 goal joined
% 0.61/1.02 % SZS status Unsatisfiable
% 0.61/1.02 #START OF PROOF
% 0.61/1.02 % SZS output start CNFRefutation
% 0.61/1.02 cnf('0.2.0.0',axiom,
% 0.61/1.02 ( X1 = add(additive_identity,X1) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.2.1.0',plain,
% 0.61/1.02 ( X1 = add(additive_identity,X1) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.61/1.02 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.61/1.02 cnf('0.2.2.0',plain,
% 0.61/1.02 ( add(additive_identity,X1) = X1 ),
% 0.61/1.02 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_2]).
% 0.61/1.02 cnf('0.3.0.0',axiom,
% 0.61/1.02 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.3.1.0',plain,
% 0.61/1.02 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.61/1.02 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.61/1.02 cnf('0.3.2.0',plain,
% 0.61/1.02 ( additive_inverse(additive_inverse(X1)) = X1 ),
% 0.61/1.02 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_3]).
% 0.61/1.02 cnf('0.5.0.0',axiom,
% 0.61/1.02 ( multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.5.1.0',plain,
% 0.61/1.02 ( multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.61/1.02 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.61/1.02 cnf('0.5.2.0',plain,
% 0.61/1.02 ( multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_5]).
% 0.61/1.02 cnf('0.6.0.0',axiom,
% 0.61/1.02 ( multiply(X1,multiply(X1,X2)) = multiply(multiply(X1,X1),X2) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.6.1.0',plain,
% 0.61/1.02 ( multiply(X1,multiply(X1,X2)) = multiply(multiply(X1,X1),X2) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.61/1.02 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.61/1.02 cnf('0.6.2.0',plain,
% 0.61/1.02 ( multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_6]).
% 0.61/1.02 cnf('0.7.0.0',axiom,
% 0.61/1.02 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.7.1.0',plain,
% 0.61/1.02 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.61/1.02 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.61/1.02 cnf('0.7.2.0',plain,
% 0.61/1.02 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.61/1.02 [u,rule_7]).
% 0.61/1.02 cnf('0.10.0.0',axiom,
% 0.61/1.02 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.10.1.0',plain,
% 0.61/1.02 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.61/1.02 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.61/1.02 cnf('0.10.2.0',plain,
% 0.61/1.02 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.61/1.02 [u,rule_10]).
% 0.61/1.02 cnf('0.14.0.0',axiom,
% 0.61/1.02 ( add(X1,X2) = add(X2,X1) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.14.1.0',plain,
% 0.61/1.02 ( add(X1,X2) = add(X2,X1) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.61/1.02 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.61/1.02 cnf('0.14.2.0',plain,
% 0.61/1.02 ( add(X1,X2) = add(X2,X1) ),
% 0.61/1.02 inference(activate,[status(thm)],['0.14.1.0']),
% 0.61/1.02 [equation_1]).
% 0.61/1.02 cnf('0.15.0.0',axiom,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.15.1.0',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.61/1.02 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.61/1.02 cnf('0.15.2.0',plain,
% 0.61/1.02 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_14]).
% 0.61/1.02 cnf('0.16.0.0',axiom,
% 0.61/1.02 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.16.1.0',plain,
% 0.61/1.02 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.61/1.02 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.61/1.02 cnf('0.16.2.0',plain,
% 0.61/1.02 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.61/1.02 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.61/1.02 [u,rule_15]).
% 0.61/1.02 cnf('0.18.0.0',axiom,
% 0.61/1.02 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019')).
% 0.61/1.02 cnf('0.18.1.0',plain,
% 0.61/1.02 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.61/1.02 [weight('<20,0,0,[0,0,0,21]>')]).
% 0.61/1.02 cnf('0.18.1.1',plain,
% 0.61/1.02 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) = associator(X1,X2,X3) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.18.1.0','0.14.2.0',theory(equality)]),
% 0.61/1.02 [pos('L','L')]).
% 0.61/1.02 cnf('0.18.2.0',plain,
% 0.61/1.02 ( associator(X1,X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.18.1.1',theory(equality)]),
% 0.61/1.02 [x,rule_17]).
% 0.61/1.02 cnf('0.20.0.0',plain,
% 0.61/1.02 ( add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.15.2.0','0.16.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1','L')]).
% 0.61/1.02 cnf('0.20.0.1',plain,
% 0.61/1.02 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.20.0.0','0.2.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('0.20.1.0',plain,
% 0.61/1.02 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.20.0.1']),
% 0.61/1.02 [weight('<6,16,15,[0,0,0,1]>')]).
% 0.61/1.02 cnf('0.20.2.0',plain,
% 0.61/1.02 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.61/1.02 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.61/1.02 [u,rule_19]).
% 0.61/1.02 cnf('0.21.0.0',plain,
% 0.61/1.02 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.20.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2.1','L')]).
% 0.61/1.02 cnf('0.21.1.0',plain,
% 0.61/1.02 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.61/1.02 [weight('<6,20,3,[1,0,0,3]>')]).
% 0.61/1.02 cnf('0.21.2.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X1,X2)) = X2 ),
% 0.61/1.02 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_20]).
% 0.61/1.02 cnf('0.23.0.0',plain,
% 0.61/1.02 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.21.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2','L')]).
% 0.61/1.02 cnf('0.23.1.0',plain,
% 0.61/1.02 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.61/1.02 [weight('<6,21,14,[1,0,0,3]>')]).
% 0.61/1.02 cnf('0.23.2.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X2,X1)) = X2 ),
% 0.61/1.02 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_22]).
% 0.61/1.02 cnf('0.30.0.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(add(X2,X1),X3)) = add(X2,X3) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.15.2.0','0.23.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1','L')]).
% 0.61/1.02 cnf('0.30.0.1',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.30.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2','L')]).
% 0.61/1.02 cnf('0.30.1.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.30.0.1']),
% 0.61/1.02 [weight('<8,23,15,[0,0,0,1]>')]).
% 0.61/1.02 cnf('0.30.2.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.61/1.02 [u,rule_29]).
% 0.61/1.02 cnf('0.31.0.0',plain,
% 0.61/1.02 ( add(X1,X2) = add(additive_inverse(X3),add(X1,add(X2,X3))) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.23.2.0','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2','L')]).
% 0.61/1.02 cnf('0.31.1.0',plain,
% 0.61/1.02 ( add(X1,X2) = add(additive_inverse(X3),add(X1,add(X2,X3))) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.61/1.02 [weight('<8,23,15,[1,0,0,3]>')]).
% 0.61/1.02 cnf('0.31.2.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X2,add(X3,X1))) = add(X2,X3) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_30]).
% 0.61/1.02 cnf('0.33.0.0',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(add(X2,X1),X3) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.15.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1','L')]).
% 0.61/1.02 cnf('0.33.0.1',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.33.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('0.33.1.0',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.61/1.02 [weight('<10,15,14,[1,0,0,1]>')]).
% 0.61/1.02 cnf('0.33.2.0',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.61/1.02 inference(activate,[status(thm)],['0.33.1.0']),
% 0.61/1.02 [equation_3]).
% 0.61/1.02 cnf('0.37.0.0',plain,
% 0.61/1.02 ( add(add(X1,X2),X3) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.31.2.0','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2','L')]).
% 0.61/1.02 cnf('0.37.0.1',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.37.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('L','L')]).
% 0.61/1.02 cnf('0.37.1.0',plain,
% 0.61/1.02 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.37.0.1']),
% 0.61/1.02 [weight('<10,31,15,[1,0,0,3]>')]).
% 0.61/1.02 cnf('0.37.2.0',plain,
% 0.61/1.02 ( add(additive_inverse(X1),add(X2,add(X3,add(X4,X1)))) = add(X2,add(X3,X4)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_34]).
% 0.61/1.02 cnf('0.39.0.0',plain,
% 0.61/1.02 ( multiply(add(X1,X2),multiply(add(X1,X2),X3)) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.6.2.0','0.7.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1','L')]).
% 0.61/1.02 cnf('0.39.1.0',plain,
% 0.61/1.02 ( multiply(add(X1,X2),multiply(add(X1,X2),X3)) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.61/1.02 [weight('<13,7,6,[0,0,0,1]>')]).
% 0.61/1.02 cnf('0.39.1.1',plain,
% 0.61/1.02 ( 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) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.0','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('L','L')]).
% 0.61/1.02 cnf('0.39.1.2',plain,
% 0.61/1.02 ( 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) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.1','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1.2','L')]).
% 0.61/1.02 cnf('0.39.1.3',plain,
% 0.61/1.02 ( 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) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.2','0.7.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1','L')]).
% 0.61/1.02 cnf('0.39.1.4',plain,
% 0.61/1.02 ( 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) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.3','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('L','L')]).
% 0.61/1.02 cnf('0.39.1.5',plain,
% 0.61/1.02 ( 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) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.4','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2.2.2','L')]).
% 0.61/1.02 cnf('0.39.1.6',plain,
% 0.61/1.02 ( 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) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.5','0.7.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2.2','L')]).
% 0.61/1.02 cnf('0.39.1.7',plain,
% 0.61/1.02 ( 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)) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.6','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('0.39.1.8',plain,
% 0.61/1.02 ( 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)) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.7','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.1.1','L')]).
% 0.61/1.02 cnf('0.39.1.9',plain,
% 0.61/1.02 ( 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)) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.8','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.1','L')]).
% 0.61/1.02 cnf('0.39.1.10',plain,
% 0.61/1.02 ( 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))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.9','0.15.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('0.39.1.11',plain,
% 0.61/1.02 ( 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))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.10','0.6.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.1','L')]).
% 0.61/1.02 cnf('0.39.1.12',plain,
% 0.61/1.02 ( 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))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.11','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.2.2.1','L')]).
% 0.61/1.02 cnf('0.39.1.13',plain,
% 0.61/1.02 ( 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)))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.12','0.10.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.2.2','L')]).
% 0.61/1.02 cnf('0.39.1.14',plain,
% 0.61/1.02 ( 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))))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.13','0.6.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.2.2.2','L')]).
% 0.61/1.02 cnf('0.39.1.15',plain,
% 0.61/1.02 ( 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)))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.14','0.14.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.2.2','L')]).
% 0.61/1.02 cnf('0.39.1.16',plain,
% 0.61/1.02 ( 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)))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.39.1.15','0.33.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.2','L')]).
% 0.61/1.02 cnf('0.39.2.0',plain,
% 0.61/1.02 ( 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)))) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.39.1.16',theory(equality)]),
% 0.61/1.02 [x,rule_35]).
% 0.61/1.02 cnf('0.40.0.0',plain,
% 0.61/1.02 ( 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))) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.39.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2','L')]).
% 0.61/1.02 cnf('0.40.1.0',plain,
% 0.61/1.02 ( 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))) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.61/1.02 [weight('<17,39,0,[1,0,0,6]>')]).
% 0.61/1.02 cnf('0.40.2.0',plain,
% 0.61/1.02 ( 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)))) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_36]).
% 0.61/1.02 cnf('0.41.0.0',plain,
% 0.61/1.02 ( 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)))))) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.30.2.0','0.40.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.2.2','L')]).
% 0.61/1.02 cnf('0.41.0.1',plain,
% 0.61/1.02 ( 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)))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['0.41.0.0','0.37.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('0.41.1.0',plain,
% 0.61/1.02 ( add(multiply(multiply(X2,X3),X4),multiply(multiply(X3,X2),X4)) = add(multiply(X2,multiply(X3,X4)),multiply(X3,multiply(X2,X4))) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.41.0.1']),
% 0.61/1.02 [weight('<11,40,30,[0,0,0,5]>')]).
% 0.61/1.02 cnf('0.41.2.0',plain,
% 0.61/1.02 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3)) = add(multiply(X1,multiply(X2,X3)),multiply(X2,multiply(X1,X3))) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.61/1.02 [u,rule_37]).
% 0.61/1.02 cnf('0.42.0.0',plain,
% 0.61/1.02 ( add(multiply(X1,multiply(X2,X2)),multiply(X2,multiply(X1,X2))) = add(multiply(X1,multiply(X2,X2)),multiply(multiply(X2,X1),X2)) ),
% 0.61/1.02 inference(cp,[status(thm)],['0.41.2.0','0.5.2.0',theory(equality)]),
% 0.61/1.02 [pos('L.1','L')]).
% 0.61/1.02 cnf('0.42.1.0',plain,
% 0.61/1.02 ( multiply(X2,multiply(X1,X2)) = multiply(multiply(X2,X1),X2) ),
% 0.61/1.02 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.61/1.02 [weight('<5,41,5,[1,0,0,1]>')]).
% 0.61/1.02 cnf('0.42.2.0',plain,
% 0.61/1.02 ( multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)) ),
% 0.61/1.02 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.61/1.02 [x,rule_38]).
% 0.61/1.02 cnf('1.0.0.0',conjecture,
% 0.61/1.02 ( additive_identity = associator(x,y,x) ),
% 0.61/1.02 file('/tmp/WALDMEISTER_9601_n019',conjecture_1)).
% 0.61/1.02 cnf('1.0.0.1',plain,
% 0.61/1.02 ( additive_identity = add(additive_inverse(multiply(x,multiply(y,x))),multiply(multiply(x,y),x)) ),
% 0.61/1.02 inference(reduction,[status(thm)],['1.0.0.0','0.18.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('1.0.0.2',plain,
% 0.61/1.02 ( additive_identity = add(additive_inverse(multiply(x,multiply(y,x))),multiply(x,multiply(y,x))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['1.0.0.1','0.42.2.0',theory(equality)]),
% 0.61/1.02 [pos('R.2','L')]).
% 0.61/1.02 cnf('1.0.0.3',plain,
% 0.61/1.02 ( additive_identity = add(multiply(x,multiply(y,x)),additive_inverse(multiply(x,multiply(y,x)))) ),
% 0.61/1.02 inference(reduction,[status(thm)],['1.0.0.2','0.14.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('1.0.0.4',plain,
% 0.61/1.02 ( additive_identity = additive_identity ),
% 0.61/1.02 inference(reduction,[status(thm)],['1.0.0.3','0.16.2.0',theory(equality)]),
% 0.61/1.02 [pos('R','L')]).
% 0.61/1.02 cnf('1.0.0.5',plain,
% 0.61/1.02 ( $true ),
% 0.61/1.02 inference(trivial,[status(thm)],['1.0.0.4',theory(equality)]),
% 0.61/1.02 [conjecture_1]).
% 0.61/1.02
% 0.61/1.02 Proved Goals:
% 0.61/1.02 No. 1: additive_identity ?= associator(x,y,x) joined, current: additive_identity = additive_identity
% 0.61/1.02 1 goal was specified, which was proved.
% 0.61/1.02 % SZS output end CNFRefutation
% 0.61/1.02 #END OF PROOF
% 0.61/1.02
% 0.61/1.02 Problem WALDMEISTER_9601_n019
% 0.61/1.02 CPs.gen 716
% 0.61/1.02 CPs.reexp 0
% 0.61/1.02 Select 267
% 0.61/1.02 R 38
% 0.61/1.02 E 4
% 0.61/1.02 vsize 6.5M
% 0.61/1.02 rss 3.8M
% 0.61/1.02 process.time 0.009s
% 0.61/1.02 wallclock.time 0.009s
% 0.61/1.02 status S
% 0.61/1.02
% 0.61/1.02
% 0.61/1.02 Waldmeister states: Goal proved.
% 0.61/1.02 % SZS status Unsatisfiable
%------------------------------------------------------------------------------