TSTP Solution File: GRP670-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP670-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n005.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 : Sat Jul 16 12:27:48 EDT 2022
% Result : Unsatisfiable 3.25s 3.64s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP670-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : woody %s
% 0.13/0.35 % Computer : n005.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 Jun 13 16:07:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.60/0.99 ********************************************************************************
% 0.60/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/0.99 * |/ | \/ | *
% 0.60/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/0.99 * A. Jaeger and B. Loechner | | *
% 0.60/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/0.99 ********************************************************************************
% 0.60/0.99
% 0.60/0.99
% 0.60/0.99 Goals:
% 0.60/0.99 ------
% 0.60/0.99
% 0.60/0.99 ( 1) mult(mult(a,mult(mult(b,c),b)),c) ?=? mult(mult(a,b),mult(mult(c,b),c))
% 0.60/0.99
% 0.60/0.99 Detected structure: Loop
% 0.60/0.99 ********************************************************************************
% 0.60/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.60/0.99 ********************************************************************************
% 0.60/0.99
% 3.25/3.64 joined goal: 1 mult(mult(a,mult(mult(b,c),b)),c) ?= mult(mult(a,b),mult(mult(c,b),c)) to mult(mult(a,b),mult(c,mult(b,c)))
% 3.25/3.64 goal joined
% 3.25/3.64 % SZS status Unsatisfiable
% 3.25/3.64 #START OF PROOF
% 3.25/3.64 % SZS output start CNFRefutation
% 3.25/3.64 cnf('0.1.0.0',axiom,
% 3.25/3.64 ( X1 = mult(X2,ld(X2,X1)) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.1.1.0',plain,
% 3.25/3.64 ( X1 = mult(X2,ld(X2,X1)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.1.0.0']),
% 3.25/3.64 [weight('<0,0,0,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.1.2.0',plain,
% 3.25/3.64 ( mult(X1,ld(X1,X2)) = X2 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_1]).
% 3.25/3.64 cnf('0.2.0.0',axiom,
% 3.25/3.64 ( X1 = mult(X1,unit) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.2.1.0',plain,
% 3.25/3.64 ( X1 = mult(X1,unit) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.2.0.0']),
% 3.25/3.64 [weight('<1,0,0,[0,0,0,2]>')]).
% 3.25/3.64 cnf('0.2.2.0',plain,
% 3.25/3.64 ( mult(X1,unit) = X1 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_2]).
% 3.25/3.64 cnf('0.3.0.0',axiom,
% 3.25/3.64 ( X1 = mult(mult(X1,X2),i(X2)) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.3.1.0',plain,
% 3.25/3.64 ( X1 = mult(mult(X1,X2),i(X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.3.0.0']),
% 3.25/3.64 [weight('<2,0,0,[0,0,0,3]>')]).
% 3.25/3.64 cnf('0.3.2.0',plain,
% 3.25/3.64 ( mult(mult(X1,X2),i(X2)) = X1 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_3]).
% 3.25/3.64 cnf('0.4.0.0',axiom,
% 3.25/3.64 ( X1 = mult(unit,X1) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.4.1.0',plain,
% 3.25/3.64 ( X1 = mult(unit,X1) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.4.0.0']),
% 3.25/3.64 [weight('<3,0,0,[0,0,0,4]>')]).
% 3.25/3.64 cnf('0.4.2.0',plain,
% 3.25/3.64 ( mult(unit,X1) = X1 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_4]).
% 3.25/3.64 cnf('0.5.0.0',axiom,
% 3.25/3.64 ( X1 = mult(i(X2),mult(X2,X1)) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.5.1.0',plain,
% 3.25/3.64 ( X1 = mult(i(X2),mult(X2,X1)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.5.0.0']),
% 3.25/3.64 [weight('<4,0,0,[0,0,0,5]>')]).
% 3.25/3.64 cnf('0.5.2.0',plain,
% 3.25/3.64 ( mult(i(X1),mult(X1,X2)) = X2 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_5]).
% 3.25/3.64 cnf('0.6.0.0',axiom,
% 3.25/3.64 ( X1 = mult(rd(X1,X2),X2) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.6.1.0',plain,
% 3.25/3.64 ( X1 = mult(rd(X1,X2),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.6.0.0']),
% 3.25/3.64 [weight('<5,0,0,[0,0,0,6]>')]).
% 3.25/3.64 cnf('0.6.2.0',plain,
% 3.25/3.64 ( mult(rd(X1,X2),X2) = X1 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_6]).
% 3.25/3.64 cnf('0.7.0.0',axiom,
% 3.25/3.64 ( X1 = rd(mult(X1,X2),X2) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.7.1.0',plain,
% 3.25/3.64 ( X1 = rd(mult(X1,X2),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.7.0.0']),
% 3.25/3.64 [weight('<6,0,0,[0,0,0,7]>')]).
% 3.25/3.64 cnf('0.7.2.0',plain,
% 3.25/3.64 ( rd(mult(X1,X2),X2) = X1 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_7]).
% 3.25/3.64 cnf('0.8.0.0',axiom,
% 3.25/3.64 ( X1 = ld(X2,mult(X2,X1)) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.8.1.0',plain,
% 3.25/3.64 ( X1 = ld(X2,mult(X2,X1)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.8.0.0']),
% 3.25/3.64 [weight('<7,0,0,[0,0,0,8]>')]).
% 3.25/3.64 cnf('0.8.2.0',plain,
% 3.25/3.64 ( ld(X1,mult(X1,X2)) = X2 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_8]).
% 3.25/3.64 cnf('0.9.0.0',axiom,
% 3.25/3.64 ( mult(mult(X1,X2),mult(X3,mult(X1,X2))) = mult(mult(mult(X1,mult(X2,X3)),X1),X2) ),
% 3.25/3.64 file('/tmp/WALDMEISTER_4832_n005')).
% 3.25/3.64 cnf('0.9.1.0',plain,
% 3.25/3.64 ( mult(mult(X1,X2),mult(X3,mult(X1,X2))) = mult(mult(mult(X1,mult(X2,X3)),X1),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.9.0.0']),
% 3.25/3.64 [weight('<8,0,0,[0,0,0,9]>')]).
% 3.25/3.64 cnf('0.9.2.0',plain,
% 3.25/3.64 ( mult(mult(mult(X1,mult(X2,X3)),X1),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_9]).
% 3.25/3.64 cnf('0.10.0.0',plain,
% 3.25/3.64 ( mult(X1,X2) = mult(X1,i(i(X2))) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.3.2.0','0.3.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.10.1.0',plain,
% 3.25/3.64 ( X2 = i(i(X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.10.0.0']),
% 3.25/3.64 [weight('<19,3,3,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.10.2.0',plain,
% 3.25/3.64 ( i(i(X1)) = X1 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_10]).
% 3.25/3.64 cnf('0.21.0.0',plain,
% 3.25/3.64 ( ld(X1,X2) = mult(i(X1),X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.21.1.0',plain,
% 3.25/3.64 ( ld(X1,X2) = mult(i(X1),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.21.0.0']),
% 3.25/3.64 [weight('<39,5,1,[1,0,0,3]>')]).
% 3.25/3.64 cnf('0.21.2.0',plain,
% 3.25/3.64 ( mult(i(X1),X2) = ld(X1,X2) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_21]).
% 3.25/3.64 cnf('0.22.0.0',plain,
% 3.25/3.64 ( rd(X1,X2) = mult(X1,i(X2)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.3.2.0','0.6.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.22.1.0',plain,
% 3.25/3.64 ( rd(X1,X2) = mult(X1,i(X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.22.0.0']),
% 3.25/3.64 [weight('<39,6,3,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.22.2.0',plain,
% 3.25/3.64 ( mult(X1,i(X2)) = rd(X1,X2) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_22]).
% 3.25/3.64 cnf('0.23.0.0',plain,
% 3.25/3.64 ( ld(i(X1),X2) = mult(X1,X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.21.2.0','0.10.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.23.1.0',plain,
% 3.25/3.64 ( ld(i(X1),X2) = mult(X1,X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.23.0.0']),
% 3.25/3.64 [weight('<39,21,10,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.23.2.0',plain,
% 3.25/3.64 ( ld(i(X1),X2) = mult(X1,X2) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_23]).
% 3.25/3.64 cnf('0.24.0.0',plain,
% 3.25/3.64 ( rd(X1,i(X2)) = mult(X1,X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.22.2.0','0.10.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.24.1.0',plain,
% 3.25/3.64 ( rd(X1,i(X2)) = mult(X1,X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.24.0.0']),
% 3.25/3.64 [weight('<39,22,10,[1,0,0,2]>')]).
% 3.25/3.64 cnf('0.24.2.0',plain,
% 3.25/3.64 ( rd(X1,i(X2)) = mult(X1,X2) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_24]).
% 3.25/3.64 cnf('0.26.0.0',plain,
% 3.25/3.64 ( X1 = ld(rd(X2,X1),X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.8.2.0','0.6.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.26.1.0',plain,
% 3.25/3.64 ( X1 = ld(rd(X2,X1),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.26.0.0']),
% 3.25/3.64 [weight('<41,8,6,[1,0,0,2]>')]).
% 3.25/3.64 cnf('0.26.2.0',plain,
% 3.25/3.64 ( ld(rd(X1,X2),X1) = X2 ),
% 3.25/3.64 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_26]).
% 3.25/3.64 cnf('0.27.0.0',plain,
% 3.25/3.64 ( rd(i(X1),X2) = ld(X1,i(X2)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.22.2.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.27.1.0',plain,
% 3.25/3.64 ( rd(i(X1),X2) = ld(X1,i(X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.27.0.0']),
% 3.25/3.64 [weight('<44,22,21,[1,0,0,0]>')]).
% 3.25/3.64 cnf('0.27.2.0',plain,
% 3.25/3.64 ( rd(i(X1),X2) = ld(X1,i(X2)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_27]).
% 3.25/3.64 cnf('0.28.0.0',plain,
% 3.25/3.64 ( i(X1) = rd(ld(X1,X2),X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.7.2.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.28.1.0',plain,
% 3.25/3.64 ( i(X1) = rd(ld(X1,X2),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.28.0.0']),
% 3.25/3.64 [weight('<47,21,7,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.28.2.0',plain,
% 3.25/3.64 ( rd(ld(X1,X2),X2) = i(X1) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_28]).
% 3.25/3.64 cnf('0.29.0.0',plain,
% 3.25/3.64 ( i(rd(X1,X2)) = rd(X2,X1) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.28.2.0','0.26.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.29.1.0',plain,
% 3.25/3.64 ( i(rd(X1,X2)) = rd(X2,X1) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.29.0.0']),
% 3.25/3.64 [weight('<39,28,26,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.29.2.0',plain,
% 3.25/3.64 ( i(rd(X1,X2)) = rd(X2,X1) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_29]).
% 3.25/3.64 cnf('0.30.0.0',plain,
% 3.25/3.64 ( rd(i(X1),X2) = i(mult(X2,X1)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.29.2.0','0.24.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.30.0.1',plain,
% 3.25/3.64 ( ld(X1,i(X2)) = i(mult(X2,X1)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.30.0.0','0.27.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.30.1.0',plain,
% 3.25/3.64 ( ld(X1,i(X2)) = i(mult(X2,X1)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.30.0.1']),
% 3.25/3.64 [weight('<44,29,24,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.30.2.0',plain,
% 3.25/3.64 ( i(mult(X1,X2)) = ld(X2,i(X1)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_30]).
% 3.25/3.64 cnf('0.31.0.0',plain,
% 3.25/3.64 ( ld(X1,i(i(X2))) = i(ld(X2,X1)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.30.2.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.31.0.1',plain,
% 3.25/3.64 ( ld(X1,X2) = i(ld(X2,X1)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.31.0.0','0.10.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.31.1.0',plain,
% 3.25/3.64 ( ld(X1,X2) = i(ld(X2,X1)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.31.0.1']),
% 3.25/3.64 [weight('<39,30,21,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.31.2.0',plain,
% 3.25/3.64 ( i(ld(X1,X2)) = ld(X2,X1) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_31]).
% 3.25/3.64 cnf('0.37.0.0',plain,
% 3.25/3.64 ( mult(mult(X1,unit),mult(X2,mult(X1,unit))) = mult(mult(X1,mult(unit,X2)),X1) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.9.2.0','0.2.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.37.0.1',plain,
% 3.25/3.64 ( mult(X1,mult(X2,mult(X1,unit))) = mult(mult(X1,mult(unit,X2)),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.37.0.0','0.2.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.37.0.2',plain,
% 3.25/3.64 ( mult(X1,mult(X2,X1)) = mult(mult(X1,mult(unit,X2)),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.37.0.1','0.2.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2.2','L')]).
% 3.25/3.64 cnf('0.37.0.3',plain,
% 3.25/3.64 ( mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.37.0.2','0.4.2.0',theory(equality)]),
% 3.25/3.64 [pos('R.1.2','L')]).
% 3.25/3.64 cnf('0.37.1.0',plain,
% 3.25/3.64 ( mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.37.0.3']),
% 3.25/3.64 [weight('<65,9,2,[1,0,0,0]>')]).
% 3.25/3.64 cnf('0.37.2.0',plain,
% 3.25/3.64 ( mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_37]).
% 3.25/3.64 cnf('0.38.0.0',plain,
% 3.25/3.64 ( ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.21.2.0','0.29.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.38.1.0',plain,
% 3.25/3.64 ( ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.38.0.0']),
% 3.25/3.64 [weight('<65,29,21,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.38.2.0',plain,
% 3.25/3.64 ( mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_38]).
% 3.25/3.64 cnf('0.39.0.0',plain,
% 3.25/3.64 ( rd(X1,rd(X2,X3)) = mult(X1,rd(X3,X2)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.22.2.0','0.29.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.39.1.0',plain,
% 3.25/3.64 ( rd(X1,rd(X2,X3)) = mult(X1,rd(X3,X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.39.0.0']),
% 3.25/3.64 [weight('<65,29,22,[0,0,0,2]>')]).
% 3.25/3.64 cnf('0.39.2.0',plain,
% 3.25/3.64 ( mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_39]).
% 3.25/3.64 cnf('0.40.0.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.21.2.0','0.31.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.40.1.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.40.0.0']),
% 3.25/3.64 [weight('<65,31,21,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.40.2.0',plain,
% 3.25/3.64 ( mult(ld(X1,X2),X3) = ld(ld(X2,X1),X3) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_40]).
% 3.25/3.64 cnf('0.41.0.0',plain,
% 3.25/3.64 ( rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.22.2.0','0.31.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.41.1.0',plain,
% 3.25/3.64 ( rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.41.0.0']),
% 3.25/3.64 [weight('<65,31,22,[0,0,0,2]>')]).
% 3.25/3.64 cnf('0.41.2.0',plain,
% 3.25/3.64 ( mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_41]).
% 3.25/3.64 cnf('0.42.0.0',plain,
% 3.25/3.64 ( mult(i(X1),mult(X2,i(X1))) = mult(ld(X1,X2),i(X1)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.37.2.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.42.0.1',plain,
% 3.25/3.64 ( ld(X1,mult(X2,i(X1))) = mult(ld(X1,X2),i(X1)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.42.0.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.42.0.2',plain,
% 3.25/3.64 ( ld(X1,rd(X2,X1)) = mult(ld(X1,X2),i(X1)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.42.0.1','0.22.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.42.0.3',plain,
% 3.25/3.64 ( ld(X1,rd(X2,X1)) = rd(ld(X1,X2),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.42.0.2','0.22.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.42.1.0',plain,
% 3.25/3.64 ( ld(X1,rd(X2,X1)) = rd(ld(X1,X2),X1) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.42.0.3']),
% 3.25/3.64 [weight('<65,37,21,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.42.2.0',plain,
% 3.25/3.64 ( rd(ld(X1,X2),X1) = ld(X1,rd(X2,X1)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_42]).
% 3.25/3.64 cnf('0.43.0.0',plain,
% 3.25/3.64 ( mult(X1,mult(i(X2),X1)) = mult(rd(X1,X2),X1) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.37.2.0','0.22.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.43.0.1',plain,
% 3.25/3.64 ( mult(X1,ld(X2,X1)) = mult(rd(X1,X2),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.43.0.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.43.1.0',plain,
% 3.25/3.64 ( mult(X1,ld(X2,X1)) = mult(rd(X1,X2),X1) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.43.0.1']),
% 3.25/3.64 [weight('<65,37,22,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.43.1.1',plain,
% 3.25/3.64 ( rd(X1,ld(X1,X2)) = mult(rd(X1,X2),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.43.1.0','0.41.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.43.1.2',plain,
% 3.25/3.64 ( rd(X1,ld(X1,X2)) = ld(rd(X2,X1),X1) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.43.1.1','0.38.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.43.2.0',plain,
% 3.25/3.64 ( rd(X1,ld(X1,X2)) = ld(rd(X2,X1),X1) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.43.1.2',theory(equality)]),
% 3.25/3.64 [u,rule_43]).
% 3.25/3.64 cnf('0.45.0.0',plain,
% 3.25/3.64 ( mult(mult(X1,X2),X3) = ld(ld(X2,i(X1)),X3) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.23.2.0','0.30.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.45.1.0',plain,
% 3.25/3.64 ( mult(mult(X1,X2),X3) = ld(ld(X2,i(X1)),X3) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.45.0.0']),
% 3.25/3.64 [weight('<83,30,23,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.45.2.0',plain,
% 3.25/3.64 ( ld(ld(X1,i(X2)),X3) = mult(mult(X2,X1),X3) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_45]).
% 3.25/3.64 cnf('0.46.0.0',plain,
% 3.25/3.64 ( mult(X1,mult(X2,X3)) = rd(X1,ld(X3,i(X2))) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.24.2.0','0.30.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.46.1.0',plain,
% 3.25/3.64 ( mult(X1,mult(X2,X3)) = rd(X1,ld(X3,i(X2))) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.46.0.0']),
% 3.25/3.64 [weight('<83,30,24,[0,0,0,2]>')]).
% 3.25/3.64 cnf('0.46.2.0',plain,
% 3.25/3.64 ( rd(X1,ld(X2,i(X3))) = mult(X1,mult(X3,X2)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_46]).
% 3.25/3.64 cnf('0.47.0.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),i(X3)) = rd(ld(X2,X1),X3) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.27.2.0','0.31.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.47.1.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),i(X3)) = rd(ld(X2,X1),X3) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.47.0.0']),
% 3.25/3.64 [weight('<83,31,27,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.47.2.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),i(X3)) = rd(ld(X2,X1),X3) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_47]).
% 3.25/3.64 cnf('0.75.0.0',plain,
% 3.25/3.64 ( rd(rd(X1,X2),ld(X3,X4)) = ld(rd(X2,X1),ld(X4,X3)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.41.2.0','0.38.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.75.1.0',plain,
% 3.25/3.64 ( rd(rd(X1,X2),ld(X3,X4)) = ld(rd(X2,X1),ld(X4,X3)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.75.0.0']),
% 3.25/3.64 [weight('<119,41,38,[1,0,0,0]>')]).
% 3.25/3.64 cnf('0.75.2.0',plain,
% 3.25/3.64 ( rd(rd(X1,X2),ld(X3,X4)) = ld(rd(X2,X1),ld(X4,X3)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_75]).
% 3.25/3.64 cnf('0.107.0.0',plain,
% 3.25/3.64 ( mult(mult(mult(X1,mult(X2,X3)),X1),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))) ),
% 3.25/3.64 inference(interreduction_right,[status(thm)],['0.9.2.0'])).
% 3.25/3.64 cnf('0.107.0.1',plain,
% 3.25/3.64 ( mult(mult(X1,mult(mult(X2,X3),X1)),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.107.0.0','0.37.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.107.1.0',plain,
% 3.25/3.64 ( mult(mult(X1,mult(mult(X2,X3),X1)),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.107.0.1']),
% 3.25/3.64 [weight('<?,9,37,[0,0,0,0]>')]).
% 3.25/3.64 cnf('0.107.2.0',plain,
% 3.25/3.64 ( mult(mult(X1,mult(mult(X2,X3),X1)),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_107]).
% 3.25/3.64 cnf('0.243.0.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),rd(i(X3),ld(X1,X2))) = rd(rd(ld(X2,X1),X3),ld(X1,X2)) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.42.2.0','0.47.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.243.0.1',plain,
% 3.25/3.64 ( ld(ld(X1,X2),ld(X3,i(ld(X1,X2)))) = rd(rd(ld(X2,X1),X3),ld(X1,X2)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.243.0.0','0.27.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.243.0.2',plain,
% 3.25/3.64 ( ld(ld(X1,X2),ld(X3,ld(X2,X1))) = rd(rd(ld(X2,X1),X3),ld(X1,X2)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.243.0.1','0.31.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2.2','L')]).
% 3.25/3.64 cnf('0.243.1.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),ld(X3,ld(X2,X1))) = rd(rd(ld(X2,X1),X3),ld(X1,X2)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.243.0.2']),
% 3.25/3.64 [weight('<189,47,42,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.243.1.1',plain,
% 3.25/3.64 ( ld(ld(X1,X2),ld(X3,ld(X2,X1))) = ld(rd(X3,ld(X2,X1)),ld(X2,X1)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.243.1.0','0.75.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.243.2.0',plain,
% 3.25/3.64 ( ld(rd(X1,ld(X2,X3)),ld(X2,X3)) = ld(ld(X3,X2),ld(X1,ld(X2,X3))) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.243.1.1',theory(equality)]),
% 3.25/3.64 [x,rule_243]).
% 3.25/3.64 cnf('0.254.0.0',plain,
% 3.25/3.64 ( mult(mult(i(X1),X2),mult(X3,mult(i(X1),X2))) = mult(ld(X1,mult(mult(X2,X3),i(X1))),X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.107.2.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.254.0.1',plain,
% 3.25/3.64 ( mult(ld(X1,X2),mult(X3,mult(i(X1),X2))) = mult(ld(X1,mult(mult(X2,X3),i(X1))),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.254.0.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.254.0.2',plain,
% 3.25/3.64 ( ld(ld(X2,X1),mult(X3,mult(i(X1),X2))) = mult(ld(X1,mult(mult(X2,X3),i(X1))),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.254.0.1','0.40.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.254.0.3',plain,
% 3.25/3.64 ( ld(ld(X2,X1),mult(X3,ld(X1,X2))) = mult(ld(X1,mult(mult(X2,X3),i(X1))),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.254.0.2','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2.2','L')]).
% 3.25/3.64 cnf('0.254.0.4',plain,
% 3.25/3.64 ( ld(ld(X2,X1),rd(X3,ld(X2,X1))) = mult(ld(X1,mult(mult(X2,X3),i(X1))),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.254.0.3','0.41.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.254.0.5',plain,
% 3.25/3.64 ( ld(ld(X2,X1),rd(X3,ld(X2,X1))) = ld(ld(mult(mult(X2,X3),i(X1)),X1),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.254.0.4','0.40.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.254.0.6',plain,
% 3.25/3.64 ( ld(ld(X2,X1),rd(X3,ld(X2,X1))) = ld(ld(rd(mult(X2,X3),X1),X1),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.254.0.5','0.22.2.0',theory(equality)]),
% 3.25/3.64 [pos('R.1.1','L')]).
% 3.25/3.64 cnf('0.254.1.0',plain,
% 3.25/3.64 ( ld(ld(X2,X1),rd(X3,ld(X2,X1))) = ld(ld(rd(mult(X2,X3),X1),X1),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.254.0.6']),
% 3.25/3.64 [weight('<189,107,21,[1,0,0,1]>')]).
% 3.25/3.64 cnf('0.254.2.0',plain,
% 3.25/3.64 ( ld(ld(rd(mult(X1,X2),X3),X3),X1) = ld(ld(X1,X3),rd(X2,ld(X1,X3))) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.254.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_254]).
% 3.25/3.64 cnf('0.332.0.0',plain,
% 3.25/3.64 ( mult(mult(X1,X2),mult(i(X3),mult(X1,X2))) = mult(mult(X1,mult(rd(X2,X3),X1)),X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.107.2.0','0.22.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1.2.1','L')]).
% 3.25/3.64 cnf('0.332.0.1',plain,
% 3.25/3.64 ( mult(mult(X1,X2),ld(X3,mult(X1,X2))) = mult(mult(X1,mult(rd(X2,X3),X1)),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.0','0.21.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.332.0.2',plain,
% 3.25/3.64 ( rd(mult(X1,X2),ld(mult(X1,X2),X3)) = mult(mult(X1,mult(rd(X2,X3),X1)),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.1','0.41.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.332.0.3',plain,
% 3.25/3.64 ( ld(rd(X3,mult(X1,X2)),mult(X1,X2)) = mult(mult(X1,mult(rd(X2,X3),X1)),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.2','0.43.2.0',theory(equality)]),
% 3.25/3.64 [pos('L','L')]).
% 3.25/3.64 cnf('0.332.0.4',plain,
% 3.25/3.64 ( ld(rd(X3,mult(X1,X2)),mult(X1,X2)) = mult(mult(X1,ld(rd(X3,X2),X1)),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.3','0.38.2.0',theory(equality)]),
% 3.25/3.64 [pos('R.1.2','L')]).
% 3.25/3.64 cnf('0.332.0.5',plain,
% 3.25/3.64 ( ld(rd(X3,mult(X1,X2)),mult(X1,X2)) = mult(rd(X1,ld(X1,rd(X3,X2))),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.4','0.41.2.0',theory(equality)]),
% 3.25/3.64 [pos('R.1','L')]).
% 3.25/3.64 cnf('0.332.0.6',plain,
% 3.25/3.64 ( ld(rd(X3,mult(X1,X2)),mult(X1,X2)) = mult(ld(rd(rd(X3,X2),X1),X1),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.5','0.43.2.0',theory(equality)]),
% 3.25/3.64 [pos('R.1','L')]).
% 3.25/3.64 cnf('0.332.0.7',plain,
% 3.25/3.64 ( ld(rd(X3,mult(X1,X2)),mult(X1,X2)) = ld(ld(X1,rd(rd(X3,X2),X1)),X2) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.332.0.6','0.40.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.332.1.0',plain,
% 3.25/3.64 ( ld(rd(X3,mult(X1,X2)),mult(X1,X2)) = ld(ld(X1,rd(rd(X3,X2),X1)),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.332.0.7']),
% 3.25/3.64 [weight('<189,107,22,[1,0,0,4]>')]).
% 3.25/3.64 cnf('0.332.2.0',plain,
% 3.25/3.64 ( ld(ld(X1,rd(rd(X2,X3),X1)),X3) = ld(rd(X2,mult(X1,X3)),mult(X1,X3)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.332.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_332]).
% 3.25/3.64 cnf('0.395.0.0',plain,
% 3.25/3.64 ( ld(X1,ld(rd(mult(X1,X2),X3),X3)) = i(ld(ld(X1,X3),rd(X2,ld(X1,X3)))) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.31.2.0','0.254.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.395.0.1',plain,
% 3.25/3.64 ( ld(X1,ld(rd(mult(X1,X2),X3),X3)) = ld(rd(X2,ld(X1,X3)),ld(X1,X3)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.395.0.0','0.31.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.395.0.2',plain,
% 3.25/3.64 ( ld(X1,ld(rd(mult(X1,X2),X3),X3)) = ld(ld(X3,X1),ld(X2,ld(X1,X3))) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.395.0.1','0.243.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.395.1.0',plain,
% 3.25/3.64 ( ld(X1,ld(rd(mult(X1,X2),X3),X3)) = ld(ld(X3,X1),ld(X2,ld(X1,X3))) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.395.0.2']),
% 3.25/3.64 [weight('<189,254,31,[0,0,0,1]>')]).
% 3.25/3.64 cnf('0.395.2.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),ld(X3,ld(X2,X1))) = ld(X2,ld(rd(mult(X2,X3),X1),X1)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.395.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_395]).
% 3.25/3.64 cnf('0.485.0.0',plain,
% 3.25/3.64 ( ld(X1,ld(rd(mult(X1,i(X2)),X3),X3)) = ld(ld(X3,X1),mult(X2,ld(X1,X3))) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.395.2.0','0.23.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2','L')]).
% 3.25/3.64 cnf('0.485.0.1',plain,
% 3.25/3.64 ( ld(X1,ld(rd(rd(X1,X2),X3),X3)) = ld(ld(X3,X1),mult(X2,ld(X1,X3))) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.485.0.0','0.22.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.2.1.1','L')]).
% 3.25/3.64 cnf('0.485.0.2',plain,
% 3.25/3.64 ( ld(X1,ld(rd(rd(X1,X2),X3),X3)) = ld(ld(X3,X1),rd(X2,ld(X3,X1))) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.485.0.1','0.41.2.0',theory(equality)]),
% 3.25/3.64 [pos('R.2','L')]).
% 3.25/3.64 cnf('0.485.1.0',plain,
% 3.25/3.64 ( ld(X1,ld(rd(rd(X1,X2),X3),X3)) = ld(ld(X3,X1),rd(X2,ld(X3,X1))) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.485.0.2']),
% 3.25/3.64 [weight('<189,395,23,[1,0,0,4]>')]).
% 3.25/3.64 cnf('0.485.2.0',plain,
% 3.25/3.64 ( ld(ld(X1,X2),rd(X3,ld(X1,X2))) = ld(X2,ld(rd(rd(X2,X3),X1),X1)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.485.1.0',theory(equality)]),
% 3.25/3.64 [x,rule_485]).
% 3.25/3.64 cnf('0.487.0.0',plain,
% 3.25/3.64 ( ld(ld(rd(mult(X1,X2),X3),X3),X1) = ld(ld(X1,X3),rd(X2,ld(X1,X3))) ),
% 3.25/3.64 inference(interreduction_right,[status(thm)],['0.254.2.0'])).
% 3.25/3.64 cnf('0.487.0.1',plain,
% 3.25/3.64 ( ld(ld(rd(mult(X1,X2),X3),X3),X1) = ld(X3,ld(rd(rd(X3,X2),X1),X1)) ),
% 3.25/3.64 inference(reduction,[status(thm)],['0.487.0.0','0.485.2.0',theory(equality)]),
% 3.25/3.64 [pos('R','L')]).
% 3.25/3.64 cnf('0.487.1.0',plain,
% 3.25/3.64 ( ld(ld(rd(mult(X1,X2),X3),X3),X1) = ld(X3,ld(rd(rd(X3,X2),X1),X1)) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.487.0.1']),
% 3.25/3.64 [weight('<189,254,485,[0,0,0,0]>')]).
% 3.25/3.64 cnf('0.487.2.0',plain,
% 3.25/3.64 ( ld(ld(rd(mult(X1,X2),X3),X3),X1) = ld(X3,ld(rd(rd(X3,X2),X1),X1)) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.487.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_487]).
% 3.25/3.64 cnf('0.948.0.0',plain,
% 3.25/3.64 ( ld(rd(mult(X1,X2),mult(X3,X2)),mult(X3,X2)) = ld(ld(X3,rd(X1,X3)),X2) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.332.2.0','0.7.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1.2.1','L')]).
% 3.25/3.64 cnf('0.948.1.0',plain,
% 3.25/3.64 ( ld(rd(mult(X1,X2),mult(X3,X2)),mult(X3,X2)) = ld(ld(X3,rd(X1,X3)),X2) ),
% 3.25/3.64 inference(weigh,[status(thm)],['0.948.0.0']),
% 3.25/3.64 [weight('<227,332,7,[1,0,0,4]>')]).
% 3.25/3.64 cnf('0.948.2.0',plain,
% 3.25/3.64 ( ld(rd(mult(X1,X2),mult(X3,X2)),mult(X3,X2)) = ld(ld(X3,rd(X1,X3)),X2) ),
% 3.25/3.64 inference(orient,[status(thm)],['0.948.1.0',theory(equality)]),
% 3.25/3.64 [u,rule_948]).
% 3.25/3.64 cnf('0.949.0.0',plain,
% 3.25/3.64 ( ld(mult(X1,X2),ld(rd(rd(mult(X1,X2),X2),X3),X3)) = ld(ld(ld(X1,rd(X3,X1)),X2),X3) ),
% 3.25/3.64 inference(cp,[status(thm)],['0.487.2.0','0.948.2.0',theory(equality)]),
% 3.25/3.64 [pos('L.1','L')]).
% 3.25/3.64 cnf('0.949.0.1',plain,
% 3.25/3.64 ( ld(mult(X1,X2),ld(rd(X1,X3),X3)) = ld(ld(ld(X1,rd(X3,X1)),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.949.0.0','0.7.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.2.1.1','L')]).
% 3.25/3.65 cnf('0.949.1.0',plain,
% 3.25/3.65 ( ld(mult(X1,X2),ld(rd(X1,X3),X3)) = ld(ld(ld(X1,rd(X3,X1)),X2),X3) ),
% 3.25/3.65 inference(weigh,[status(thm)],['0.949.0.1']),
% 3.25/3.65 [weight('<189,948,487,[0,0,0,1]>')]).
% 3.25/3.65 cnf('0.949.2.0',plain,
% 3.25/3.65 ( ld(ld(ld(X1,rd(X2,X1)),X3),X2) = ld(mult(X1,X3),ld(rd(X1,X2),X2)) ),
% 3.25/3.65 inference(orient,[status(thm)],['0.949.1.0',theory(equality)]),
% 3.25/3.65 [x,rule_949]).
% 3.25/3.65 cnf('0.951.0.0',plain,
% 3.25/3.65 ( ld(mult(i(X1),X2),ld(rd(i(X1),X3),X3)) = ld(ld(mult(X1,rd(X3,i(X1))),X2),X3) ),
% 3.25/3.65 inference(cp,[status(thm)],['0.949.2.0','0.23.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.1.1','L')]).
% 3.25/3.65 cnf('0.951.0.1',plain,
% 3.25/3.65 ( ld(ld(X1,X2),ld(rd(i(X1),X3),X3)) = ld(ld(mult(X1,rd(X3,i(X1))),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.0','0.21.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.1','L')]).
% 3.25/3.65 cnf('0.951.0.2',plain,
% 3.25/3.65 ( ld(ld(X1,X2),ld(ld(X1,i(X3)),X3)) = ld(ld(mult(X1,rd(X3,i(X1))),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.1','0.27.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.2.1','L')]).
% 3.25/3.65 cnf('0.951.0.3',plain,
% 3.25/3.65 ( ld(ld(X1,X2),mult(mult(X3,X1),X3)) = ld(ld(mult(X1,rd(X3,i(X1))),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.2','0.45.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.2','L')]).
% 3.25/3.65 cnf('0.951.0.4',plain,
% 3.25/3.65 ( ld(ld(X1,X2),mult(X3,mult(X1,X3))) = ld(ld(mult(X1,rd(X3,i(X1))),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.3','0.37.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.2','L')]).
% 3.25/3.65 cnf('0.951.0.5',plain,
% 3.25/3.65 ( ld(ld(X1,X2),mult(X3,mult(X1,X3))) = ld(ld(rd(X1,rd(i(X1),X3)),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.4','0.39.2.0',theory(equality)]),
% 3.25/3.65 [pos('R.1.1','L')]).
% 3.25/3.65 cnf('0.951.0.6',plain,
% 3.25/3.65 ( ld(ld(X1,X2),mult(X3,mult(X1,X3))) = ld(ld(rd(X1,ld(X1,i(X3))),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.5','0.27.2.0',theory(equality)]),
% 3.25/3.65 [pos('R.1.1.2','L')]).
% 3.25/3.65 cnf('0.951.0.7',plain,
% 3.25/3.65 ( ld(ld(X1,X2),mult(X3,mult(X1,X3))) = ld(ld(mult(X1,mult(X3,X1)),X2),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.951.0.6','0.46.2.0',theory(equality)]),
% 3.25/3.65 [pos('R.1.1','L')]).
% 3.25/3.65 cnf('0.951.1.0',plain,
% 3.25/3.65 ( ld(ld(X1,X2),mult(X3,mult(X1,X3))) = ld(ld(mult(X1,mult(X3,X1)),X2),X3) ),
% 3.25/3.65 inference(weigh,[status(thm)],['0.951.0.7']),
% 3.25/3.65 [weight('<189,949,23,[1,0,0,2]>')]).
% 3.25/3.65 cnf('0.951.2.0',plain,
% 3.25/3.65 ( ld(ld(mult(X1,mult(X2,X1)),X3),X2) = ld(ld(X1,X3),mult(X2,mult(X1,X2))) ),
% 3.25/3.65 inference(orient,[status(thm)],['0.951.1.0',theory(equality)]),
% 3.25/3.65 [x,rule_951]).
% 3.25/3.65 cnf('0.966.0.0',plain,
% 3.25/3.65 ( ld(ld(X1,i(X2)),mult(X3,mult(X1,X3))) = mult(mult(X2,mult(X1,mult(X3,X1))),X3) ),
% 3.25/3.65 inference(cp,[status(thm)],['0.951.2.0','0.45.2.0',theory(equality)]),
% 3.25/3.65 [pos('L','L')]).
% 3.25/3.65 cnf('0.966.0.1',plain,
% 3.25/3.65 ( mult(mult(X2,X1),mult(X3,mult(X1,X3))) = mult(mult(X2,mult(X1,mult(X3,X1))),X3) ),
% 3.25/3.65 inference(reduction,[status(thm)],['0.966.0.0','0.45.2.0',theory(equality)]),
% 3.25/3.65 [pos('L','L')]).
% 3.25/3.65 cnf('0.966.1.0',plain,
% 3.25/3.65 ( mult(mult(X2,X1),mult(X3,mult(X1,X3))) = mult(mult(X2,mult(X1,mult(X3,X1))),X3) ),
% 3.25/3.65 inference(weigh,[status(thm)],['0.966.0.1']),
% 3.25/3.65 [weight('<189,951,45,[1,0,0,0]>')]).
% 3.25/3.65 cnf('0.966.2.0',plain,
% 3.25/3.65 ( mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))) ),
% 3.25/3.65 inference(orient,[status(thm)],['0.966.1.0',theory(equality)]),
% 3.25/3.65 [x,rule_966]).
% 3.25/3.65 cnf('1.0.0.0',conjecture,
% 3.25/3.65 ( mult(mult(a,mult(mult(b,c),b)),c) = mult(mult(a,b),mult(mult(c,b),c)) ),
% 3.25/3.65 file('/tmp/WALDMEISTER_4832_n005',conjecture_1)).
% 3.25/3.65 cnf('1.0.0.1',plain,
% 3.25/3.65 ( mult(mult(a,mult(b,mult(c,b))),c) = mult(mult(a,b),mult(mult(c,b),c)) ),
% 3.25/3.65 inference(reduction,[status(thm)],['1.0.0.0','0.37.2.0',theory(equality)]),
% 3.25/3.65 [pos('L.1.2','L')]).
% 3.25/3.65 cnf('1.0.0.2',plain,
% 3.25/3.65 ( mult(mult(a,mult(b,mult(c,b))),c) = mult(mult(a,b),mult(c,mult(b,c))) ),
% 3.25/3.65 inference(reduction,[status(thm)],['1.0.0.1','0.37.2.0',theory(equality)]),
% 3.25/3.65 [pos('R.2','L')]).
% 3.25/3.65 cnf('1.0.0.3',plain,
% 3.25/3.65 ( mult(mult(a,b),mult(c,mult(b,c))) = mult(mult(a,b),mult(c,mult(b,c))) ),
% 3.25/3.65 inference(reduction,[status(thm)],['1.0.0.2','0.966.2.0',theory(equality)]),
% 3.25/3.65 [pos('L','L')]).
% 3.25/3.65 cnf('1.0.0.4',plain,
% 3.25/3.65 ( $true ),
% 3.25/3.65 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 3.25/3.65 [conjecture_1]).
% 3.25/3.65
% 3.25/3.65 Proved Goals:
% 3.25/3.65 No. 1: mult(mult(a,mult(mult(b,c),b)),c) ?= mult(mult(a,b),mult(mult(c,b),c)) joined, current: mult(mult(a,b),mult(c,mult(b,c))) = mult(mult(a,b),mult(c,mult(b,c)))
% 3.25/3.65 1 goal was specified, which was proved.
% 3.25/3.65 % SZS output end CNFRefutation
% 3.25/3.65 #END OF PROOF
% 3.25/3.65
% 3.25/3.65 Problem WALDMEISTER_4832_n005
% 3.25/3.65 CPs.gen 360498
% 3.25/3.65 CPs.reexp 0
% 3.25/3.65 Select 6999
% 3.25/3.65 R 966
% 3.25/3.65 E 0
% 3.25/3.65 vsize 8.6M
% 3.25/3.65 rss 4.2M
% 3.25/3.65 process.time 2.656s
% 3.25/3.65 wallclock.time 2.656s
% 3.25/3.65 status S
% 3.25/3.65
% 3.25/3.65
% 3.25/3.65 Waldmeister states: Goal proved.
% 3.25/3.65 % SZS status Unsatisfiable
%------------------------------------------------------------------------------