TSTP Solution File: RNG025-5 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : RNG025-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n021.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 1.14s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG025-5 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n021.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 19:03:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.97 * |/ | \/ | *
% 0.57/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.97 * A. Jaeger and B. Loechner | | *
% 0.57/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.57/0.97
% 0.57/0.97 Goals:
% 0.57/0.97 ------
% 0.57/0.97
% 0.57/0.97 ( 1) add(associator(x,y,z),associator(x,z,y)) ?=? additive_identity
% 0.57/0.97
% 0.57/0.97 Detected structure: NichtassoziativerRing
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.61/1.14 joined goal: 1 add(associator(x,y,z),associator(x,z,y)) ?= additive_identity to additive_identity
% 0.61/1.14 goal joined
% 0.61/1.14 % SZS status Unsatisfiable
% 0.61/1.14 #START OF PROOF
% 0.61/1.14 % SZS output start CNFRefutation
% 0.61/1.14 cnf('0.1.0.0',axiom,
% 0.61/1.14 ( X1 = add(X1,additive_identity) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.1.1.0',plain,
% 0.61/1.14 ( X1 = add(X1,additive_identity) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.61/1.14 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.61/1.14 cnf('0.1.2.0',plain,
% 0.61/1.14 ( add(X1,additive_identity) = X1 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_1]).
% 0.61/1.14 cnf('0.2.0.0',axiom,
% 0.61/1.14 ( X1 = add(additive_identity,X1) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.2.1.0',plain,
% 0.61/1.14 ( X1 = add(additive_identity,X1) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.61/1.14 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.61/1.14 cnf('0.2.2.0',plain,
% 0.61/1.14 ( add(additive_identity,X1) = X1 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_2]).
% 0.61/1.14 cnf('0.3.0.0',axiom,
% 0.61/1.14 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.3.1.0',plain,
% 0.61/1.14 ( X1 = additive_inverse(additive_inverse(X1)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.61/1.14 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.61/1.14 cnf('0.3.2.0',plain,
% 0.61/1.14 ( additive_inverse(additive_inverse(X1)) = X1 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_3]).
% 0.61/1.14 cnf('0.5.0.0',axiom,
% 0.61/1.14 ( multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.5.1.0',plain,
% 0.61/1.14 ( multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.61/1.14 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.61/1.14 cnf('0.5.2.0',plain,
% 0.61/1.14 ( multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_5]).
% 0.61/1.14 cnf('0.6.0.0',axiom,
% 0.61/1.14 ( multiply(X1,multiply(X1,X2)) = multiply(multiply(X1,X1),X2) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.6.1.0',plain,
% 0.61/1.14 ( multiply(X1,multiply(X1,X2)) = multiply(multiply(X1,X1),X2) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.61/1.14 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.61/1.14 cnf('0.6.2.0',plain,
% 0.61/1.14 ( multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_6]).
% 0.61/1.14 cnf('0.7.0.0',axiom,
% 0.61/1.14 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.7.1.0',plain,
% 0.61/1.14 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.61/1.14 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.61/1.14 cnf('0.7.2.0',plain,
% 0.61/1.14 ( multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_7]).
% 0.61/1.14 cnf('0.8.0.0',axiom,
% 0.61/1.14 ( multiply(X1,add(X2,additive_inverse(X3))) = add(multiply(X1,X2),additive_inverse(multiply(X1,X3))) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.8.1.0',plain,
% 0.61/1.14 ( multiply(X1,add(X2,additive_inverse(X3))) = add(multiply(X1,X2),additive_inverse(multiply(X1,X3))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.61/1.14 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.61/1.14 cnf('0.8.1.1',plain,
% 0.61/1.14 ( add(multiply(X1,X2),multiply(X1,additive_inverse(X3))) = add(multiply(X1,X2),additive_inverse(multiply(X1,X3))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.8.1.0','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.8.2.0',plain,
% 0.61/1.14 ( multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.8.1.1',theory(equality)]),
% 0.61/1.14 [u,rule_8]).
% 0.61/1.14 cnf('0.10.0.0',axiom,
% 0.61/1.14 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.10.1.0',plain,
% 0.61/1.14 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.61/1.14 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.61/1.14 cnf('0.10.2.0',plain,
% 0.61/1.14 ( multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_10]).
% 0.61/1.14 cnf('0.11.0.0',axiom,
% 0.61/1.14 ( multiply(add(X1,additive_inverse(X2)),X3) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.11.1.0',plain,
% 0.61/1.14 ( multiply(add(X1,additive_inverse(X2)),X3) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.61/1.14 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.61/1.14 cnf('0.11.1.1',plain,
% 0.61/1.14 ( add(multiply(X1,X3),multiply(additive_inverse(X2),X3)) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.11.1.0','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.11.2.0',plain,
% 0.61/1.14 ( multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.11.1.1',theory(equality)]),
% 0.61/1.14 [u,rule_11]).
% 0.61/1.14 cnf('0.14.0.0',axiom,
% 0.61/1.14 ( add(X1,X2) = add(X2,X1) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.14.1.0',plain,
% 0.61/1.14 ( add(X1,X2) = add(X2,X1) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.61/1.14 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.61/1.14 cnf('0.14.2.0',plain,
% 0.61/1.14 ( add(X1,X2) = add(X2,X1) ),
% 0.61/1.14 inference(activate,[status(thm)],['0.14.1.0']),
% 0.61/1.14 [equation_1]).
% 0.61/1.14 cnf('0.15.0.0',axiom,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.15.1.0',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(add(X1,X2),X3) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.61/1.14 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.61/1.14 cnf('0.15.2.0',plain,
% 0.61/1.14 ( add(add(X1,X2),X3) = add(X1,add(X2,X3)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_14]).
% 0.61/1.14 cnf('0.16.0.0',axiom,
% 0.61/1.14 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.16.1.0',plain,
% 0.61/1.14 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.61/1.14 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.61/1.14 cnf('0.16.2.0',plain,
% 0.61/1.14 ( add(X1,additive_inverse(X1)) = additive_identity ),
% 0.61/1.14 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_15]).
% 0.61/1.14 cnf('0.18.0.0',axiom,
% 0.61/1.14 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.61/1.14 file('/tmp/WALDMEISTER_23789_n021')).
% 0.61/1.14 cnf('0.18.1.0',plain,
% 0.61/1.14 ( add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = associator(X1,X2,X3) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.61/1.14 [weight('<20,0,0,[0,0,0,21]>')]).
% 0.61/1.14 cnf('0.18.1.1',plain,
% 0.61/1.14 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) = associator(X1,X2,X3) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.18.1.0','0.14.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.18.2.0',plain,
% 0.61/1.14 ( associator(X1,X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(multiply(X1,X2),X3)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.18.1.1',theory(equality)]),
% 0.61/1.14 [x,rule_17]).
% 0.61/1.14 cnf('0.20.0.0',plain,
% 0.61/1.14 ( add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.15.2.0','0.16.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.20.0.1',plain,
% 0.61/1.14 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.20.0.0','0.2.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.20.1.0',plain,
% 0.61/1.14 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.20.0.1']),
% 0.61/1.14 [weight('<6,16,15,[0,0,0,1]>')]).
% 0.61/1.14 cnf('0.20.2.0',plain,
% 0.61/1.14 ( add(X1,add(additive_inverse(X1),X2)) = X2 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_19]).
% 0.61/1.14 cnf('0.21.0.0',plain,
% 0.61/1.14 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.20.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2.1','L')]).
% 0.61/1.14 cnf('0.21.1.0',plain,
% 0.61/1.14 ( X1 = add(additive_inverse(X2),add(X2,X1)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.61/1.14 [weight('<6,20,3,[1,0,0,3]>')]).
% 0.61/1.14 cnf('0.21.2.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X1,X2)) = X2 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_20]).
% 0.61/1.14 cnf('0.22.0.0',plain,
% 0.61/1.14 ( X1 = add(X2,add(X1,additive_inverse(X2))) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.20.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.22.1.0',plain,
% 0.61/1.14 ( X1 = add(X2,add(X1,additive_inverse(X2))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.61/1.14 [weight('<6,20,14,[1,0,0,2]>')]).
% 0.61/1.14 cnf('0.22.2.0',plain,
% 0.61/1.14 ( add(X1,add(X2,additive_inverse(X1))) = X2 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_21]).
% 0.61/1.14 cnf('0.23.0.0',plain,
% 0.61/1.14 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.21.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.23.1.0',plain,
% 0.61/1.14 ( X1 = add(additive_inverse(X2),add(X1,X2)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.61/1.14 [weight('<6,21,14,[1,0,0,3]>')]).
% 0.61/1.14 cnf('0.23.2.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,X1)) = X2 ),
% 0.61/1.14 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_22]).
% 0.61/1.14 cnf('0.30.0.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(add(X2,X1),X3)) = add(X2,X3) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.15.2.0','0.23.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.30.0.1',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.30.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.30.1.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.30.0.1']),
% 0.61/1.14 [weight('<8,23,15,[0,0,0,1]>')]).
% 0.61/1.14 cnf('0.30.2.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X2,X3) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_29]).
% 0.61/1.14 cnf('0.31.0.0',plain,
% 0.61/1.14 ( add(X1,X2) = add(additive_inverse(X3),add(X1,add(X2,X3))) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.23.2.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.31.1.0',plain,
% 0.61/1.14 ( add(X1,X2) = add(additive_inverse(X3),add(X1,add(X2,X3))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.61/1.14 [weight('<8,23,15,[1,0,0,3]>')]).
% 0.61/1.14 cnf('0.31.2.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,add(X3,X1))) = add(X2,X3) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_30]).
% 0.61/1.14 cnf('0.33.0.0',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(add(X2,X1),X3) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.15.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.33.0.1',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.33.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.33.1.0',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.61/1.14 [weight('<10,15,14,[1,0,0,1]>')]).
% 0.61/1.14 cnf('0.33.2.0',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(X2,add(X1,X3)) ),
% 0.61/1.14 inference(activate,[status(thm)],['0.33.1.0']),
% 0.61/1.14 [equation_3]).
% 0.61/1.14 cnf('0.36.0.0',plain,
% 0.61/1.14 ( add(add(X1,X2),X3) = add(additive_inverse(X4),add(X1,add(X2,add(X4,X3)))) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.30.2.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.36.0.1',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X4,X3)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.36.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.36.1.0',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X4,X3)))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.36.0.1']),
% 0.61/1.14 [weight('<10,30,15,[1,0,0,3]>')]).
% 0.61/1.14 cnf('0.36.2.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,add(X3,add(X1,X4)))) = add(X2,add(X3,X4)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_33]).
% 0.61/1.14 cnf('0.37.0.0',plain,
% 0.61/1.14 ( add(add(X1,X2),X3) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.31.2.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.37.0.1',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.37.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.37.1.0',plain,
% 0.61/1.14 ( add(X1,add(X2,X3)) = add(additive_inverse(X4),add(X1,add(X2,add(X3,X4)))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.37.0.1']),
% 0.61/1.14 [weight('<10,31,15,[1,0,0,3]>')]).
% 0.61/1.14 cnf('0.37.2.0',plain,
% 0.61/1.14 ( add(additive_inverse(X1),add(X2,add(X3,add(X4,X1)))) = add(X2,add(X3,X4)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_34]).
% 0.61/1.14 cnf('0.39.0.0',plain,
% 0.61/1.14 ( multiply(add(X1,X2),multiply(add(X1,X2),X3)) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.6.2.0','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.39.1.0',plain,
% 0.61/1.14 ( multiply(add(X1,X2),multiply(add(X1,X2),X3)) = multiply(add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X2)),X3) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.61/1.14 [weight('<13,7,6,[0,0,0,1]>')]).
% 0.61/1.14 cnf('0.39.1.1',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.0','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.39.1.2',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.1','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1.2','L')]).
% 0.61/1.14 cnf('0.39.1.3',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.2','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.39.1.4',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.3','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.39.1.5',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.4','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2.2.2','L')]).
% 0.61/1.14 cnf('0.39.1.6',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.5','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2.2','L')]).
% 0.61/1.14 cnf('0.39.1.7',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.6','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.39.1.8',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.7','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.1.1','L')]).
% 0.61/1.14 cnf('0.39.1.9',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.8','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.1','L')]).
% 0.61/1.14 cnf('0.39.1.10',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.9','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.39.1.11',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.10','0.6.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.1','L')]).
% 0.61/1.14 cnf('0.39.1.12',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.11','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.2.2.1','L')]).
% 0.61/1.14 cnf('0.39.1.13',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.12','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.2.2','L')]).
% 0.61/1.14 cnf('0.39.1.14',plain,
% 0.61/1.14 ( 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))))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.13','0.6.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.2.2.2','L')]).
% 0.61/1.14 cnf('0.39.1.15',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.14','0.14.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.2.2','L')]).
% 0.61/1.14 cnf('0.39.1.16',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.39.1.15','0.33.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.2','L')]).
% 0.61/1.14 cnf('0.39.2.0',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.39.1.16',theory(equality)]),
% 0.61/1.14 [x,rule_35]).
% 0.61/1.14 cnf('0.40.0.0',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.39.2.0','0.14.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2','L')]).
% 0.61/1.14 cnf('0.40.1.0',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.61/1.14 [weight('<17,39,0,[1,0,0,6]>')]).
% 0.61/1.14 cnf('0.40.2.0',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_36]).
% 0.61/1.14 cnf('0.41.0.0',plain,
% 0.61/1.14 ( 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)))))) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.30.2.0','0.40.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2.2','L')]).
% 0.61/1.14 cnf('0.41.0.1',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.41.0.0','0.37.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.41.1.0',plain,
% 0.61/1.14 ( add(multiply(multiply(X2,X3),X4),multiply(multiply(X3,X2),X4)) = add(multiply(X2,multiply(X3,X4)),multiply(X3,multiply(X2,X4))) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.41.0.1']),
% 0.61/1.14 [weight('<11,40,30,[0,0,0,5]>')]).
% 0.61/1.14 cnf('0.41.2.0',plain,
% 0.61/1.14 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3)) = add(multiply(X1,multiply(X2,X3)),multiply(X2,multiply(X1,X3))) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_37]).
% 0.61/1.14 cnf('0.42.0.0',plain,
% 0.61/1.14 ( add(multiply(X1,multiply(X2,X2)),multiply(X2,multiply(X1,X2))) = add(multiply(X1,multiply(X2,X2)),multiply(multiply(X2,X1),X2)) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.41.2.0','0.5.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.42.1.0',plain,
% 0.61/1.14 ( multiply(X2,multiply(X1,X2)) = multiply(multiply(X2,X1),X2) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.61/1.14 [weight('<5,41,5,[1,0,0,1]>')]).
% 0.61/1.14 cnf('0.42.2.0',plain,
% 0.61/1.14 ( multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.61/1.14 [x,rule_38]).
% 0.61/1.14 cnf('0.48.0.0',plain,
% 0.61/1.14 ( 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) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.15.2.0','0.41.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.48.0.1',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.48.0.0','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.48.1.0',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(weigh,[status(thm)],['0.48.0.1']),
% 0.61/1.14 [weight('<13,41,15,[0,0,0,1]>')]).
% 0.61/1.14 cnf('0.48.2.0',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 0.61/1.14 [u,rule_44]).
% 0.61/1.14 cnf('0.61.0.0',plain,
% 0.61/1.14 ( multiply(add(X1,X2),multiply(X3,add(X1,X2))) = multiply(add(multiply(X1,X3),multiply(X2,X3)),add(X1,X2)) ),
% 0.61/1.14 inference(cp,[status(thm)],['0.42.2.0','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.61.0.1',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.0','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.61.0.2',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.1','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1.2','L')]).
% 0.61/1.14 cnf('0.61.0.3',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.2','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.1','L')]).
% 0.61/1.14 cnf('0.61.0.4',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.3','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('L','L')]).
% 0.61/1.14 cnf('0.61.0.5',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.4','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2.2.2','L')]).
% 0.61/1.14 cnf('0.61.0.6',plain,
% 0.61/1.14 ( 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)) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.5','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('L.2.2','L')]).
% 0.61/1.14 cnf('0.61.0.7',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.6','0.10.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.61.0.8',plain,
% 0.61/1.14 ( 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))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.7','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.1','L')]).
% 0.61/1.14 cnf('0.61.0.9',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.8','0.15.2.0',theory(equality)]),
% 0.61/1.14 [pos('R','L')]).
% 0.61/1.14 cnf('0.61.0.10',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.9','0.42.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.1','L')]).
% 0.61/1.14 cnf('0.61.0.11',plain,
% 0.61/1.14 ( 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)))) ),
% 0.61/1.14 inference(reduction,[status(thm)],['0.61.0.10','0.7.2.0',theory(equality)]),
% 0.61/1.14 [pos('R.2.2','L')]).
% 0.61/1.14 cnf('0.61.0.12',plain,
% 0.61/1.14 ( 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))))) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.61.0.11','0.42.2.0',theory(equality)]),
% 0.61/1.15 [pos('R.2.2.2','L')]).
% 0.61/1.15 cnf('0.61.1.0',plain,
% 0.61/1.15 ( 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)))) ),
% 0.61/1.15 inference(weigh,[status(thm)],['0.61.0.12']),
% 0.61/1.15 [weight('<17,42,10,[1,0,0,1]>')]).
% 0.61/1.15 cnf('0.61.1.1',plain,
% 0.61/1.15 ( 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))) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.61.1.0','0.14.2.0',theory(equality)]),
% 0.61/1.15 [pos('R.2','L')]).
% 0.61/1.15 cnf('0.61.2.0',plain,
% 0.61/1.15 ( 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)))) ),
% 0.61/1.15 inference(orient,[status(thm)],['0.61.1.1',theory(equality)]),
% 0.61/1.15 [x,rule_57]).
% 0.61/1.15 cnf('0.62.0.0',plain,
% 0.61/1.15 ( 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))))) ),
% 0.61/1.15 inference(cp,[status(thm)],['0.30.2.0','0.61.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('0.62.0.1',plain,
% 0.61/1.15 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X2,X1))) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.62.0.0','0.31.2.0',theory(equality)]),
% 0.61/1.15 [pos('R','L')]).
% 0.61/1.15 cnf('0.62.1.0',plain,
% 0.61/1.15 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X2,X1))) ),
% 0.61/1.15 inference(weigh,[status(thm)],['0.62.0.1']),
% 0.61/1.15 [weight('<11,61,30,[0,0,0,3]>')]).
% 0.61/1.15 cnf('0.62.2.0',plain,
% 0.61/1.15 ( add(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X2),X1)) = add(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X2,X1))) ),
% 0.61/1.15 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 0.61/1.15 [u,rule_58]).
% 0.61/1.15 cnf('0.67.0.0',plain,
% 0.61/1.15 ( add(multiply(X1,multiply(X2,additive_inverse(X3))),multiply(additive_inverse(X3),multiply(X2,X1))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),multiply(multiply(additive_inverse(X3),X2),X1)) ),
% 0.61/1.15 inference(cp,[status(thm)],['0.62.2.0','0.8.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.1','L')]).
% 0.61/1.15 cnf('0.67.0.1',plain,
% 0.61/1.15 ( add(multiply(X1,additive_inverse(multiply(X2,X3))),multiply(additive_inverse(X3),multiply(X2,X1))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),multiply(multiply(additive_inverse(X3),X2),X1)) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.67.0.0','0.8.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.1.2','L')]).
% 0.61/1.15 cnf('0.67.0.2',plain,
% 0.61/1.15 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),multiply(additive_inverse(X3),multiply(X2,X1))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),multiply(multiply(additive_inverse(X3),X2),X1)) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.67.0.1','0.8.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.1','L')]).
% 0.61/1.15 cnf('0.67.0.3',plain,
% 0.61/1.15 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),multiply(multiply(additive_inverse(X3),X2),X1)) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.67.0.2','0.11.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('0.67.0.4',plain,
% 0.61/1.15 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),multiply(additive_inverse(multiply(X3,X2)),X1)) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.67.0.3','0.11.2.0',theory(equality)]),
% 0.61/1.15 [pos('R.2.1','L')]).
% 0.61/1.15 cnf('0.67.0.5',plain,
% 0.61/1.15 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),additive_inverse(multiply(multiply(X3,X2),X1))) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.67.0.4','0.11.2.0',theory(equality)]),
% 0.61/1.15 [pos('R.2','L')]).
% 0.61/1.15 cnf('0.67.1.0',plain,
% 0.61/1.15 ( add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X3,multiply(X2,X1)))) = add(additive_inverse(multiply(multiply(X1,X2),X3)),additive_inverse(multiply(multiply(X3,X2),X1))) ),
% 0.61/1.15 inference(weigh,[status(thm)],['0.67.0.5']),
% 0.61/1.15 [weight('<13,62,8,[1,0,0,1]>')]).
% 0.61/1.15 cnf('0.67.2.0',plain,
% 0.61/1.15 ( 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)))) ),
% 0.61/1.15 inference(orient,[status(thm)],['0.67.1.0',theory(equality)]),
% 0.61/1.15 [x,rule_63]).
% 0.61/1.15 cnf('0.150.0.0',plain,
% 0.61/1.15 ( 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) ),
% 0.61/1.15 inference(cp,[status(thm)],['0.48.2.0','0.16.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('0.150.0.1',plain,
% 0.61/1.15 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = multiply(multiply(X1,X2),X3) ),
% 0.61/1.15 inference(reduction,[status(thm)],['0.150.0.0','0.1.2.0',theory(equality)]),
% 0.61/1.15 [pos('R','L')]).
% 0.61/1.15 cnf('0.150.1.0',plain,
% 0.61/1.15 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = multiply(multiply(X1,X2),X3) ),
% 0.61/1.15 inference(weigh,[status(thm)],['0.150.0.1']),
% 0.61/1.15 [weight('<23,48,16,[1,0,0,6]>')]).
% 0.61/1.15 cnf('0.150.2.0',plain,
% 0.61/1.15 ( add(multiply(X1,multiply(X2,X3)),add(multiply(X2,multiply(X1,X3)),additive_inverse(multiply(multiply(X2,X1),X3)))) = multiply(multiply(X1,X2),X3) ),
% 0.61/1.15 inference(activate,[status(thm)],['0.150.1.0']),
% 0.61/1.15 [equation_6]).
% 0.61/1.15 cnf('1.0.0.0',conjecture,
% 0.61/1.15 ( add(associator(x,y,z),associator(x,z,y)) = additive_identity ),
% 0.61/1.15 file('/tmp/WALDMEISTER_23789_n021',conjecture_1)).
% 0.61/1.15 cnf('1.0.0.1',plain,
% 0.61/1.15 ( add(add(additive_inverse(multiply(x,multiply(y,z))),multiply(multiply(x,y),z)),associator(x,z,y)) = additive_identity ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.0','0.18.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.1','L')]).
% 0.61/1.15 cnf('1.0.0.2',plain,
% 0.61/1.15 ( add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(multiply(x,y),z),associator(x,z,y))) = additive_identity ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.1','0.15.2.0',theory(equality)]),
% 0.61/1.15 [pos('L','L')]).
% 0.61/1.15 cnf('1.0.0.3',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.2','0.150.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.1','R')]).
% 0.61/1.15 cnf('1.0.0.4',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.3','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.1','L')]).
% 0.61/1.15 cnf('1.0.0.5',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.4','0.15.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('1.0.0.6',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.5','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L','L')]).
% 0.61/1.15 cnf('1.0.0.7',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.6','0.15.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2','L')]).
% 0.61/1.15 cnf('1.0.0.8',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.7','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('1.0.0.9',plain,
% 0.61/1.15 ( add(multiply(y,multiply(x,z)),add(additive_inverse(multiply(multiply(y,x),z)),associator(x,z,y))) = additive_identity ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.8','0.20.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('1.0.0.10',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.9','0.18.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2','L')]).
% 0.61/1.15 cnf('1.0.0.11',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.10','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('1.0.0.12',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.11','0.150.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2.2','R')]).
% 0.61/1.15 cnf('1.0.0.13',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.12','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2.2','L')]).
% 0.61/1.15 cnf('1.0.0.14',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.13','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2','L')]).
% 0.61/1.15 cnf('1.0.0.15',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.14','0.36.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('1.0.0.16',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.15','0.33.2.0',theory(equality)]),
% 0.61/1.15 [pos('L','L')]).
% 0.61/1.15 cnf('1.0.0.17',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.16','0.67.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2','L')]).
% 0.61/1.15 cnf('1.0.0.18',plain,
% 0.61/1.15 ( 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 ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.17','0.14.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2.2','L')]).
% 0.61/1.15 cnf('1.0.0.19',plain,
% 0.61/1.15 ( add(multiply(z,multiply(x,y)),additive_inverse(multiply(z,multiply(x,y)))) = additive_identity ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.18','0.22.2.0',theory(equality)]),
% 0.61/1.15 [pos('L.2','L')]).
% 0.61/1.15 cnf('1.0.0.20',plain,
% 0.61/1.15 ( additive_identity = additive_identity ),
% 0.61/1.15 inference(reduction,[status(thm)],['1.0.0.19','0.16.2.0',theory(equality)]),
% 0.61/1.15 [pos('L','L')]).
% 0.61/1.15 cnf('1.0.0.21',plain,
% 0.61/1.15 ( $true ),
% 0.61/1.15 inference(trivial,[status(thm)],['1.0.0.20',theory(equality)]),
% 0.61/1.15 [conjecture_1]).
% 0.61/1.15
% 0.61/1.15 Proved Goals:
% 0.61/1.15 No. 1: add(associator(x,y,z),associator(x,z,y)) ?= additive_identity joined, current: additive_identity = additive_identity
% 0.61/1.15 1 goal was specified, which was proved.
% 0.61/1.15 % SZS output end CNFRefutation
% 0.61/1.15 #END OF PROOF
% 0.61/1.15
% 0.61/1.15 Problem WALDMEISTER_23789_n021
% 0.61/1.15 CPs.gen 11240
% 0.61/1.15 CPs.reexp 0
% 0.61/1.15 Select 859
% 0.61/1.15 R 144
% 0.61/1.15 E 6
% 0.61/1.15 vsize 6.7M
% 0.61/1.15 rss 3.9M
% 0.61/1.15 process.time 0.172s
% 0.61/1.15 wallclock.time 0.172s
% 0.61/1.15 status S
% 0.61/1.15
% 0.61/1.15
% 0.61/1.15 Waldmeister states: Goal proved.
% 0.61/1.15 % SZS status Unsatisfiable
%------------------------------------------------------------------------------