TSTP Solution File: GRP668-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP668-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n025.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 12:27:47 EDT 2022
% Result : Unsatisfiable 1.40s 1.78s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : GRP668-1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : woody %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 18:21:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.62/1.02 ********************************************************************************
% 0.62/1.02 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/1.02 * |/ | \/ | *
% 0.62/1.02 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/1.02 * A. Jaeger and B. Loechner | | *
% 0.62/1.02 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/1.02 ********************************************************************************
% 0.62/1.02
% 0.62/1.02
% 0.62/1.02 Goals:
% 0.62/1.02 ------
% 0.62/1.02
% 0.62/1.02 ( 1) mult(mult(a,mult(mult(b,c),b)),c) ?=? mult(mult(a,b),mult(mult(c,b),c))
% 0.62/1.02
% 0.62/1.02 Detected structure: Loop
% 0.62/1.02 ********************************************************************************
% 0.62/1.02 ****************************** COMPLETION - PROOF ******************************
% 0.62/1.02 ********************************************************************************
% 0.62/1.02
% 1.40/1.78 joined goal: 1 mult(mult(a,mult(mult(b,c),b)),c) ?= mult(mult(a,b),mult(mult(c,b),c)) to mult(a,mult(b,mult(c,mult(b,c))))
% 1.40/1.78 goal joined
% 1.40/1.78 % SZS status Unsatisfiable
% 1.40/1.78 #START OF PROOF
% 1.40/1.78 % SZS output start CNFRefutation
% 1.40/1.78 cnf('0.1.0.0',axiom,
% 1.40/1.78 ( X1 = mult(X2,ld(X2,X1)) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.1.1.0',plain,
% 1.40/1.78 ( X1 = mult(X2,ld(X2,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.40/1.78 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.1.2.0',plain,
% 1.40/1.78 ( mult(X1,ld(X1,X2)) = X2 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_1]).
% 1.40/1.78 cnf('0.2.0.0',axiom,
% 1.40/1.78 ( X1 = mult(X1,unit) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.2.1.0',plain,
% 1.40/1.78 ( X1 = mult(X1,unit) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.40/1.78 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.40/1.78 cnf('0.2.2.0',plain,
% 1.40/1.78 ( mult(X1,unit) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_2]).
% 1.40/1.78 cnf('0.3.0.0',axiom,
% 1.40/1.78 ( X1 = mult(unit,X1) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.3.1.0',plain,
% 1.40/1.78 ( X1 = mult(unit,X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.40/1.78 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.40/1.78 cnf('0.3.2.0',plain,
% 1.40/1.78 ( mult(unit,X1) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_3]).
% 1.40/1.78 cnf('0.4.0.0',axiom,
% 1.40/1.78 ( X1 = mult(rd(X1,X2),X2) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.4.1.0',plain,
% 1.40/1.78 ( X1 = mult(rd(X1,X2),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.40/1.78 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.40/1.78 cnf('0.4.2.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),X2) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_4]).
% 1.40/1.78 cnf('0.5.0.0',axiom,
% 1.40/1.78 ( X1 = rd(mult(X1,X2),X2) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.5.1.0',plain,
% 1.40/1.78 ( X1 = rd(mult(X1,X2),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.40/1.78 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.40/1.78 cnf('0.5.2.0',plain,
% 1.40/1.78 ( rd(mult(X1,X2),X2) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_5]).
% 1.40/1.78 cnf('0.6.0.0',axiom,
% 1.40/1.78 ( X1 = ld(X2,mult(X2,X1)) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.6.1.0',plain,
% 1.40/1.78 ( X1 = ld(X2,mult(X2,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.6.0.0']),
% 1.40/1.78 [weight('<5,0,0,[0,0,0,6]>')]).
% 1.40/1.78 cnf('0.6.2.0',plain,
% 1.40/1.78 ( ld(X1,mult(X1,X2)) = X2 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_6]).
% 1.40/1.78 cnf('0.7.0.0',axiom,
% 1.40/1.78 ( mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.7.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.7.0.0']),
% 1.40/1.78 [weight('<6,0,0,[0,0,0,7]>')]).
% 1.40/1.78 cnf('0.7.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_7]).
% 1.40/1.78 cnf('0.8.0.0',axiom,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025')).
% 1.40/1.78 cnf('0.8.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.8.0.0']),
% 1.40/1.78 [weight('<7,0,0,[0,0,0,8]>')]).
% 1.40/1.78 cnf('0.8.2.0',plain,
% 1.40/1.78 ( mult(mult(mult(X1,X2),X2),X3) = mult(X1,mult(X2,mult(X2,X3))) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_8]).
% 1.40/1.78 cnf('0.9.0.0',plain,
% 1.40/1.78 ( ld(unit,X1) = X1 ),
% 1.40/1.78 inference(cp,[status(thm)],['0.3.2.0','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.9.1.0',plain,
% 1.40/1.78 ( ld(unit,X1) = X1 ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.9.0.0']),
% 1.40/1.78 [weight('<19,3,1,[1,0,0,0]>')]).
% 1.40/1.78 cnf('0.9.2.0',plain,
% 1.40/1.78 ( ld(unit,X1) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_9]).
% 1.40/1.78 cnf('0.10.0.0',plain,
% 1.40/1.78 ( X1 = rd(X1,unit) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.4.2.0','0.2.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.10.1.0',plain,
% 1.40/1.78 ( X1 = rd(X1,unit) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.10.0.0']),
% 1.40/1.78 [weight('<19,4,2,[1,0,0,0]>')]).
% 1.40/1.78 cnf('0.10.2.0',plain,
% 1.40/1.78 ( rd(X1,unit) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_10]).
% 1.40/1.78 cnf('0.12.0.0',plain,
% 1.40/1.78 ( unit = ld(X1,X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.12.1.0',plain,
% 1.40/1.78 ( unit = ld(X1,X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.12.0.0']),
% 1.40/1.78 [weight('<19,6,2,[1,0,0,2]>')]).
% 1.40/1.78 cnf('0.12.2.0',plain,
% 1.40/1.78 ( ld(X1,X1) = unit ),
% 1.40/1.78 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_12]).
% 1.40/1.78 cnf('0.14.0.0',plain,
% 1.40/1.78 ( X1 = ld(rd(X2,X1),X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.6.2.0','0.4.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.14.1.0',plain,
% 1.40/1.78 ( X1 = ld(rd(X2,X1),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.14.0.0']),
% 1.40/1.78 [weight('<41,6,4,[1,0,0,2]>')]).
% 1.40/1.78 cnf('0.14.2.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),X1) = X2 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_14]).
% 1.40/1.78 cnf('0.15.0.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X2,unit))) = mult(mult(X1,X2),X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.8.2.0','0.2.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.15.0.1',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.15.0.0','0.2.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2.2','L')]).
% 1.40/1.78 cnf('0.15.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.15.0.1']),
% 1.40/1.78 [weight('<65,8,2,[1,0,0,0]>')]).
% 1.40/1.78 cnf('0.15.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_15]).
% 1.40/1.78 cnf('0.16.0.0',plain,
% 1.40/1.78 ( mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.7.2.0','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.16.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.16.0.0']),
% 1.40/1.78 [weight('<87,7,1,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.16.2.0',plain,
% 1.40/1.78 ( mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_16]).
% 1.40/1.78 cnf('0.17.0.0',plain,
% 1.40/1.78 ( mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.6.2.0','0.16.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.17.1.0',plain,
% 1.40/1.78 ( mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.17.0.0']),
% 1.40/1.78 [weight('<65,16,6,[0,0,0,2]>')]).
% 1.40/1.78 cnf('0.17.2.0',plain,
% 1.40/1.78 ( mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_17]).
% 1.40/1.78 cnf('0.20.0.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.15.2.0','0.4.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.20.1.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.20.0.0']),
% 1.40/1.78 [weight('<87,15,4,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.20.2.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_20]).
% 1.40/1.78 cnf('0.22.0.0',plain,
% 1.40/1.78 ( ld(X1,X2) = rd(ld(X1,mult(X2,X1)),X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.5.2.0','0.17.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.22.1.0',plain,
% 1.40/1.78 ( ld(X1,X2) = rd(ld(X1,mult(X2,X1)),X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.22.0.0']),
% 1.40/1.78 [weight('<87,17,5,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.22.2.0',plain,
% 1.40/1.78 ( rd(ld(X1,mult(X2,X1)),X1) = ld(X1,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_22]).
% 1.40/1.78 cnf('0.23.0.0',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(ld(X1,X1),X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.22.2.0','0.3.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1.2','L')]).
% 1.40/1.78 cnf('0.23.0.1',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(unit,X1) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.23.0.0','0.12.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.1','L')]).
% 1.40/1.78 cnf('0.23.1.0',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(unit,X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.23.0.1']),
% 1.40/1.78 [weight('<27,22,3,[1,0,0,3]>')]).
% 1.40/1.78 cnf('0.23.2.0',plain,
% 1.40/1.78 ( rd(unit,X1) = ld(X1,unit) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_23]).
% 1.40/1.78 cnf('0.37.0.0',plain,
% 1.40/1.78 ( mult(X1,X1) = ld(rd(X2,X1),mult(X2,X1)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.6.2.0','0.20.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.37.1.0',plain,
% 1.40/1.78 ( mult(X1,X1) = ld(rd(X2,X1),mult(X2,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.37.0.0']),
% 1.40/1.78 [weight('<87,20,6,[0,0,0,2]>')]).
% 1.40/1.78 cnf('0.37.2.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),mult(X1,X2)) = mult(X2,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_37]).
% 1.40/1.78 cnf('0.50.0.0',plain,
% 1.40/1.78 ( mult(mult(mult(X1,X2),X2),X3) = mult(X1,mult(X2,mult(X2,X3))) ),
% 1.40/1.78 inference(interreduction_right,[status(thm)],['0.8.2.0'])).
% 1.40/1.78 cnf('0.50.0.1',plain,
% 1.40/1.78 ( mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.50.0.0','0.15.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.50.1.0',plain,
% 1.40/1.78 ( mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.50.0.1']),
% 1.40/1.78 [weight('<119,8,15,[0,0,0,0]>')]).
% 1.40/1.78 cnf('0.50.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_50]).
% 1.40/1.78 cnf('0.97.0.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.50.2.0','0.20.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.97.1.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.97.0.0']),
% 1.40/1.78 [weight('<149,50,20,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.97.2.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.97.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_97]).
% 1.40/1.78 cnf('0.98.0.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,X2),mult(X2,X3)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.97.2.0','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2.2','L')]).
% 1.40/1.78 cnf('0.98.1.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,X2),mult(X2,X3)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.98.0.0']),
% 1.40/1.78 [weight('<119,97,1,[1,0,0,6]>')]).
% 1.40/1.78 cnf('0.98.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,X2),mult(X2,X3)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_98]).
% 1.40/1.78 cnf('0.99.0.0',plain,
% 1.40/1.78 ( mult(rd(unit,X1),mult(X1,X2)) = mult(X1,ld(X1,X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.98.2.0','0.3.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.99.0.1',plain,
% 1.40/1.78 ( mult(ld(X1,unit),mult(X1,X2)) = mult(X1,ld(X1,X2)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.99.0.0','0.23.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.99.0.2',plain,
% 1.40/1.78 ( mult(ld(X1,unit),mult(X1,X2)) = X2 ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.99.0.1','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.99.1.0',plain,
% 1.40/1.78 ( mult(ld(X1,unit),mult(X1,X2)) = X2 ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.99.0.2']),
% 1.40/1.78 [weight('<71,98,3,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.99.2.0',plain,
% 1.40/1.78 ( mult(ld(X1,unit),mult(X1,X2)) = X2 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_99]).
% 1.40/1.78 cnf('0.100.0.0',plain,
% 1.40/1.78 ( ld(X1,X2) = mult(ld(X1,unit),X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.99.2.0','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.100.1.0',plain,
% 1.40/1.78 ( ld(X1,X2) = mult(ld(X1,unit),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.100.0.0']),
% 1.40/1.78 [weight('<53,99,1,[1,0,0,4]>')]).
% 1.40/1.78 cnf('0.100.2.0',plain,
% 1.40/1.78 ( mult(ld(X1,unit),X2) = ld(X1,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.100.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_100]).
% 1.40/1.78 cnf('0.101.0.0',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(ld(X1,X2),X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.5.2.0','0.100.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.101.1.0',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(ld(X1,X2),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.101.0.0']),
% 1.40/1.78 [weight('<53,100,5,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.101.2.0',plain,
% 1.40/1.78 ( rd(ld(X1,X2),X2) = ld(X1,unit) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.101.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_101]).
% 1.40/1.78 cnf('0.102.0.0',plain,
% 1.40/1.78 ( ld(rd(unit,X1),X2) = mult(X1,X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.100.2.0','0.14.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.102.0.1',plain,
% 1.40/1.78 ( ld(ld(X1,unit),X2) = mult(X1,X2) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.102.0.0','0.23.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.102.1.0',plain,
% 1.40/1.78 ( ld(ld(X1,unit),X2) = mult(X1,X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.102.0.1']),
% 1.40/1.78 [weight('<53,100,14,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.102.2.0',plain,
% 1.40/1.78 ( ld(ld(X1,unit),X2) = mult(X1,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_102]).
% 1.40/1.78 cnf('0.103.0.0',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(X2,mult(X1,X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.101.2.0','0.6.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.103.1.0',plain,
% 1.40/1.78 ( ld(X1,unit) = rd(X2,mult(X1,X2)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.103.0.0']),
% 1.40/1.78 [weight('<53,101,6,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.103.2.0',plain,
% 1.40/1.78 ( rd(X1,mult(X2,X1)) = ld(X2,unit) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.103.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_103]).
% 1.40/1.78 cnf('0.104.0.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),unit) = rd(X2,X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.101.2.0','0.14.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.104.1.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),unit) = rd(X2,X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.104.0.0']),
% 1.40/1.78 [weight('<53,101,14,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.104.2.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),unit) = rd(X2,X1) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.104.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_104]).
% 1.40/1.78 cnf('0.108.0.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.100.2.0','0.104.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.108.1.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.108.0.0']),
% 1.40/1.78 [weight('<65,104,100,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.108.2.0',plain,
% 1.40/1.78 ( mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_108]).
% 1.40/1.78 cnf('0.124.0.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),ld(rd(X2,X1),X3)) = X3 ),
% 1.40/1.78 inference(cp,[status(thm)],['0.108.2.0','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.124.1.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),ld(rd(X2,X1),X3)) = X3 ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.124.0.0']),
% 1.40/1.78 [weight('<109,108,1,[1,0,0,0]>')]).
% 1.40/1.78 cnf('0.124.2.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),ld(rd(X2,X1),X3)) = X3 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_124]).
% 1.40/1.78 cnf('0.128.0.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,X2),mult(X2,X3)) ),
% 1.40/1.78 inference(interreduction_right,[status(thm)],['0.98.2.0'])).
% 1.40/1.78 cnf('0.128.0.1',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.128.0.0','0.108.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.128.1.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.128.0.1']),
% 1.40/1.78 [weight('<119,98,108,[0,0,0,0]>')]).
% 1.40/1.78 cnf('0.128.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.128.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_128]).
% 1.40/1.78 cnf('0.129.0.0',plain,
% 1.40/1.78 ( ld(rd(rd(X1,X2),X3),mult(rd(X1,X2),unit)) = mult(mult(X3,rd(X1,X2)),rd(X2,X1)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.128.2.0','0.104.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.129.0.1',plain,
% 1.40/1.78 ( ld(rd(rd(X1,X2),X3),ld(rd(X2,X1),unit)) = mult(mult(X3,rd(X1,X2)),rd(X2,X1)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.129.0.0','0.108.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.129.0.2',plain,
% 1.40/1.78 ( ld(rd(rd(X1,X2),X3),rd(X1,X2)) = mult(mult(X3,rd(X1,X2)),rd(X2,X1)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.129.0.1','0.104.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.129.0.3',plain,
% 1.40/1.78 ( X3 = mult(mult(X3,rd(X1,X2)),rd(X2,X1)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.129.0.2','0.14.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.129.1.0',plain,
% 1.40/1.78 ( X3 = mult(mult(X3,rd(X1,X2)),rd(X2,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.129.0.3']),
% 1.40/1.78 [weight('<109,128,104,[1,0,0,4]>')]).
% 1.40/1.78 cnf('0.129.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,rd(X2,X3)),rd(X3,X2)) = X1 ),
% 1.40/1.78 inference(orient,[status(thm)],['0.129.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_129]).
% 1.40/1.78 cnf('0.130.0.0',plain,
% 1.40/1.78 ( mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.5.2.0','0.129.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.130.1.0',plain,
% 1.40/1.78 ( mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.130.0.0']),
% 1.40/1.78 [weight('<65,129,5,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.130.2.0',plain,
% 1.40/1.78 ( mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.130.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_130]).
% 1.40/1.78 cnf('0.131.0.0',plain,
% 1.40/1.78 ( rd(X1,rd(X2,mult(X3,X2))) = mult(X1,X3) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.130.2.0','0.5.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.131.0.1',plain,
% 1.40/1.78 ( rd(X1,ld(X3,unit)) = mult(X1,X3) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.131.0.0','0.103.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.131.1.0',plain,
% 1.40/1.78 ( rd(X1,ld(X3,unit)) = mult(X1,X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.131.0.1']),
% 1.40/1.78 [weight('<53,130,5,[1,0,0,2]>')]).
% 1.40/1.78 cnf('0.131.2.0',plain,
% 1.40/1.78 ( rd(X1,ld(X2,unit)) = mult(X1,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.131.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_131]).
% 1.40/1.78 cnf('0.132.0.0',plain,
% 1.40/1.78 ( rd(X1,rd(X2,unit)) = mult(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.130.2.0','0.23.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.132.0.1',plain,
% 1.40/1.78 ( rd(X1,X2) = mult(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.132.0.0','0.10.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.132.1.0',plain,
% 1.40/1.78 ( rd(X1,X2) = mult(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.132.0.1']),
% 1.40/1.78 [weight('<53,130,23,[1,0,0,2]>')]).
% 1.40/1.78 cnf('0.132.2.0',plain,
% 1.40/1.78 ( mult(X1,ld(X2,unit)) = rd(X1,X2) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.132.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_132]).
% 1.40/1.78 cnf('0.133.0.0',plain,
% 1.40/1.78 ( ld(X1,unit) = ld(mult(X2,X1),X2) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.14.2.0','0.131.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.133.1.0',plain,
% 1.40/1.78 ( ld(X1,unit) = ld(mult(X2,X1),X2) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.133.0.0']),
% 1.40/1.78 [weight('<53,131,14,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.133.2.0',plain,
% 1.40/1.78 ( ld(mult(X1,X2),X1) = ld(X2,unit) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_133]).
% 1.40/1.78 cnf('0.134.0.0',plain,
% 1.40/1.78 ( ld(X1,unit) = ld(X2,rd(X2,X1)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.6.2.0','0.132.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.134.1.0',plain,
% 1.40/1.78 ( ld(X1,unit) = ld(X2,rd(X2,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.134.0.0']),
% 1.40/1.78 [weight('<53,132,6,[0,0,0,2]>')]).
% 1.40/1.78 cnf('0.134.2.0',plain,
% 1.40/1.78 ( ld(X1,rd(X1,X2)) = ld(X2,unit) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_134]).
% 1.40/1.78 cnf('0.135.0.0',plain,
% 1.40/1.78 ( ld(ld(X1,X2),unit) = ld(X2,X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.133.2.0','0.1.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.135.1.0',plain,
% 1.40/1.78 ( ld(ld(X1,X2),unit) = ld(X2,X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.135.0.0']),
% 1.40/1.78 [weight('<53,133,1,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.135.2.0',plain,
% 1.40/1.78 ( ld(ld(X1,X2),unit) = ld(X2,X1) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.135.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_135]).
% 1.40/1.78 cnf('0.138.0.0',plain,
% 1.40/1.78 ( rd(ld(X1,unit),X2) = ld(mult(X2,X1),unit) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.104.2.0','0.131.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.138.1.0',plain,
% 1.40/1.78 ( rd(ld(X1,unit),X2) = ld(mult(X2,X1),unit) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.138.0.0']),
% 1.40/1.78 [weight('<65,131,104,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.138.2.0',plain,
% 1.40/1.78 ( rd(ld(X1,unit),X2) = ld(mult(X2,X1),unit) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.138.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_138]).
% 1.40/1.78 cnf('0.140.0.0',plain,
% 1.40/1.78 ( rd(ld(X1,unit),X2) = ld(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.132.2.0','0.100.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.140.1.0',plain,
% 1.40/1.78 ( rd(ld(X1,unit),X2) = ld(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.140.0.0']),
% 1.40/1.78 [weight('<65,132,100,[1,0,0,0]>')]).
% 1.40/1.78 cnf('0.140.1.1',plain,
% 1.40/1.78 ( ld(mult(X2,X1),unit) = ld(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.140.1.0','0.138.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.140.2.0',plain,
% 1.40/1.78 ( ld(mult(X1,X2),unit) = ld(X2,ld(X1,unit)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.140.1.1',theory(equality)]),
% 1.40/1.78 [u,rule_140]).
% 1.40/1.78 cnf('0.141.0.0',plain,
% 1.40/1.78 ( ld(mult(X1,X2),unit) = rd(ld(X2,unit),X1) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.101.2.0','0.133.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.141.1.0',plain,
% 1.40/1.78 ( ld(mult(X1,X2),unit) = rd(ld(X2,unit),X1) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.141.0.0']),
% 1.40/1.78 [weight('<65,133,101,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.141.1.1',plain,
% 1.40/1.78 ( ld(X2,ld(X1,unit)) = rd(ld(X2,unit),X1) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.141.1.0','0.140.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.141.2.0',plain,
% 1.40/1.78 ( rd(ld(X1,unit),X2) = ld(X1,ld(X2,unit)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.141.1.1',theory(equality)]),
% 1.40/1.78 [x,rule_141]).
% 1.40/1.78 cnf('0.143.0.0',plain,
% 1.40/1.78 ( ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.100.2.0','0.135.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.143.1.0',plain,
% 1.40/1.78 ( ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.143.0.0']),
% 1.40/1.78 [weight('<65,135,100,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.143.2.0',plain,
% 1.40/1.78 ( mult(ld(X1,X2),X3) = ld(ld(X2,X1),X3) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.143.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_143]).
% 1.40/1.78 cnf('0.145.0.0',plain,
% 1.40/1.78 ( mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.131.2.0','0.135.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.145.1.0',plain,
% 1.40/1.78 ( mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.145.0.0']),
% 1.40/1.78 [weight('<65,135,131,[0,0,0,2]>')]).
% 1.40/1.78 cnf('0.145.2.0',plain,
% 1.40/1.78 ( mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.145.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_145]).
% 1.40/1.78 cnf('0.158.0.0',plain,
% 1.40/1.78 ( ld(rd(ld(X1,unit),X2),X3) = mult(mult(X2,X1),X3) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.108.2.0','0.131.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.158.1.0',plain,
% 1.40/1.78 ( ld(rd(ld(X1,unit),X2),X3) = mult(mult(X2,X1),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.158.0.0']),
% 1.40/1.78 [weight('<103,131,108,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.158.1.1',plain,
% 1.40/1.78 ( ld(ld(X1,ld(X2,unit)),X3) = mult(mult(X2,X1),X3) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.158.1.0','0.141.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.158.2.0',plain,
% 1.40/1.78 ( ld(ld(X1,ld(X2,unit)),X3) = mult(mult(X2,X1),X3) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.158.1.1',theory(equality)]),
% 1.40/1.78 [u,rule_158]).
% 1.40/1.78 cnf('0.161.0.0',plain,
% 1.40/1.78 ( rd(rd(X1,X2),X3) = ld(rd(X2,X1),ld(X3,unit)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.124.2.0','0.134.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.161.1.0',plain,
% 1.40/1.78 ( rd(rd(X1,X2),X3) = ld(rd(X2,X1),ld(X3,unit)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.161.0.0']),
% 1.40/1.78 [weight('<103,134,124,[0,0,0,4]>')]).
% 1.40/1.78 cnf('0.161.2.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),ld(X3,unit)) = rd(rd(X2,X1),X3) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.161.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_161]).
% 1.40/1.78 cnf('0.175.0.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),mult(X1,X2)) = ld(ld(X1,unit),mult(X2,mult(X1,X2))) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.37.2.0','0.103.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.175.0.1',plain,
% 1.40/1.78 ( mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.175.0.0','0.102.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.175.1.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.175.0.1']),
% 1.40/1.78 [weight('<119,103,37,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.175.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.175.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_175]).
% 1.40/1.78 cnf('0.180.0.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),ld(X2,X3)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(interreduction_right,[status(thm)],['0.128.2.0'])).
% 1.40/1.78 cnf('0.180.0.1',plain,
% 1.40/1.78 ( rd(mult(X1,X2),ld(X3,X2)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.180.0.0','0.145.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.180.1.0',plain,
% 1.40/1.78 ( rd(mult(X1,X2),ld(X3,X2)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.180.0.1']),
% 1.40/1.78 [weight('<119,128,145,[0,0,0,0]>')]).
% 1.40/1.78 cnf('0.180.2.0',plain,
% 1.40/1.78 ( rd(mult(X1,X2),ld(X3,X2)) = ld(rd(X2,X1),mult(X2,X3)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.180.1.0',theory(equality)]),
% 1.40/1.78 [u,rule_180]).
% 1.40/1.78 cnf('0.187.0.0',plain,
% 1.40/1.78 ( ld(mult(X1,X2),ld(X3,unit)) = rd(ld(X2,ld(X1,unit)),X3) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.141.2.0','0.140.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.187.1.0',plain,
% 1.40/1.78 ( ld(mult(X1,X2),ld(X3,unit)) = rd(ld(X2,ld(X1,unit)),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.187.0.0']),
% 1.40/1.78 [weight('<119,141,140,[1,0,0,1]>')]).
% 1.40/1.78 cnf('0.187.2.0',plain,
% 1.40/1.78 ( rd(ld(X1,ld(X2,unit)),X3) = ld(mult(X2,X1),ld(X3,unit)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.187.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_187]).
% 1.40/1.78 cnf('0.205.0.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),mult(X1,ld(X3,unit))) = rd(mult(X2,X1),mult(X3,X1)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.180.2.0','0.102.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.205.0.1',plain,
% 1.40/1.78 ( ld(rd(X1,X2),rd(X1,ld(unit,X3))) = rd(mult(X2,X1),mult(X3,X1)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.205.0.0','0.145.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.205.0.2',plain,
% 1.40/1.78 ( ld(rd(X1,X2),rd(X1,X3)) = rd(mult(X2,X1),mult(X3,X1)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.205.0.1','0.9.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2.2','L')]).
% 1.40/1.78 cnf('0.205.1.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),rd(X1,X3)) = rd(mult(X2,X1),mult(X3,X1)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.205.0.2']),
% 1.40/1.78 [weight('<119,180,102,[1,0,0,4]>')]).
% 1.40/1.78 cnf('0.205.2.0',plain,
% 1.40/1.78 ( rd(mult(X1,X2),mult(X3,X2)) = ld(rd(X2,X1),rd(X2,X3)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.205.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_205]).
% 1.40/1.78 cnf('0.254.0.0',plain,
% 1.40/1.78 ( ld(rd(X1,X2),rd(X1,mult(X3,X1))) = rd(mult(X2,X1),mult(X3,mult(X1,X1))) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.205.2.0','0.15.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.254.0.1',plain,
% 1.40/1.78 ( ld(rd(X1,X2),ld(X3,unit)) = rd(mult(X2,X1),mult(X3,mult(X1,X1))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.254.0.0','0.103.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.254.0.2',plain,
% 1.40/1.78 ( rd(rd(X2,X1),X3) = rd(mult(X2,X1),mult(X3,mult(X1,X1))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.254.0.1','0.161.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('0.254.1.0',plain,
% 1.40/1.78 ( rd(rd(X2,X1),X3) = rd(mult(X2,X1),mult(X3,mult(X1,X1))) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.254.0.2']),
% 1.40/1.78 [weight('<149,205,15,[1,0,0,4]>')]).
% 1.40/1.78 cnf('0.254.2.0',plain,
% 1.40/1.78 ( rd(mult(X1,X2),mult(X3,mult(X2,X2))) = rd(rd(X1,X2),X3) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.254.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_254]).
% 1.40/1.78 cnf('0.273.0.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = ld(rd(rd(X3,X2),X1),mult(X3,X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.14.2.0','0.254.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1','L')]).
% 1.40/1.78 cnf('0.273.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = ld(rd(rd(X3,X2),X1),mult(X3,X2)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.273.0.0']),
% 1.40/1.78 [weight('<149,254,14,[0,0,0,1]>')]).
% 1.40/1.78 cnf('0.273.2.0',plain,
% 1.40/1.78 ( ld(rd(rd(X1,X2),X3),mult(X1,X2)) = mult(X3,mult(X2,X2)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.273.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_273]).
% 1.40/1.78 cnf('0.339.0.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = ld(rd(ld(X3,ld(X2,unit)),X1),mult(ld(X3,unit),X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.273.2.0','0.141.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1.1','L')]).
% 1.40/1.78 cnf('0.339.0.1',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = ld(ld(mult(X2,X3),ld(X1,unit)),mult(ld(X3,unit),X2)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.339.0.0','0.187.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.1','L')]).
% 1.40/1.78 cnf('0.339.0.2',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = mult(mult(X1,mult(X2,X3)),mult(ld(X3,unit),X2)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.339.0.1','0.158.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.339.0.3',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = mult(mult(X1,mult(X2,X3)),ld(ld(unit,X3),X2)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.339.0.2','0.143.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.2','L')]).
% 1.40/1.78 cnf('0.339.0.4',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,X3)),ld(X2,ld(unit,X3))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.339.0.3','0.145.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.339.0.5',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,X3)),ld(X2,X3)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.339.0.4','0.9.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.2.2','L')]).
% 1.40/1.78 cnf('0.339.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,X3)),ld(X2,X3)) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.339.0.5']),
% 1.40/1.78 [weight('<149,273,141,[1,0,0,2]>')]).
% 1.40/1.78 cnf('0.339.2.0',plain,
% 1.40/1.78 ( rd(mult(X1,mult(X2,X3)),ld(X2,X3)) = mult(X1,mult(X2,X2)) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.339.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_339]).
% 1.40/1.78 cnf('0.505.0.0',plain,
% 1.40/1.78 ( mult(X1,mult(mult(X2,X3),mult(X2,X3))) = ld(rd(ld(X2,unit),X1),mult(X3,mult(X2,X3))) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.273.2.0','0.103.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1.1','L')]).
% 1.40/1.78 cnf('0.505.0.1',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = ld(rd(ld(X2,unit),X1),mult(X3,mult(X2,X3))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.505.0.0','0.175.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.505.0.2',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = ld(ld(X2,ld(X1,unit)),mult(X3,mult(X2,X3))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.505.0.1','0.141.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.1','L')]).
% 1.40/1.78 cnf('0.505.0.3',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = mult(mult(X1,X2),mult(X3,mult(X2,X3))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.505.0.2','0.158.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.505.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = mult(mult(X1,X2),mult(X3,mult(X2,X3))) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.505.0.3']),
% 1.40/1.78 [weight('<189,273,103,[1,0,0,2]>')]).
% 1.40/1.78 cnf('0.505.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.505.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_505]).
% 1.40/1.78 cnf('0.620.0.0',plain,
% 1.40/1.78 ( mult(X1,mult(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,mult(X2,mult(X3,X2))),ld(mult(X2,X3),X2)) ),
% 1.40/1.78 inference(cp,[status(thm)],['0.339.2.0','0.7.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1.2','L')]).
% 1.40/1.78 cnf('0.620.0.1',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = rd(mult(X1,mult(X2,mult(X3,X2))),ld(mult(X2,X3),X2)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.620.0.0','0.175.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.2','L')]).
% 1.40/1.78 cnf('0.620.0.2',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = rd(mult(X1,mult(X2,mult(X3,X2))),ld(X3,unit)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.620.0.1','0.133.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.2','L')]).
% 1.40/1.78 cnf('0.620.0.3',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = mult(mult(X1,mult(X2,mult(X3,X2))),X3) ),
% 1.40/1.78 inference(reduction,[status(thm)],['0.620.0.2','0.131.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('0.620.1.0',plain,
% 1.40/1.78 ( mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = mult(mult(X1,mult(X2,mult(X3,X2))),X3) ),
% 1.40/1.78 inference(weigh,[status(thm)],['0.620.0.3']),
% 1.40/1.78 [weight('<189,339,7,[1,0,0,3]>')]).
% 1.40/1.78 cnf('0.620.2.0',plain,
% 1.40/1.78 ( mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))) ),
% 1.40/1.78 inference(orient,[status(thm)],['0.620.1.0',theory(equality)]),
% 1.40/1.78 [x,rule_620]).
% 1.40/1.78 cnf('1.0.0.0',conjecture,
% 1.40/1.78 ( mult(mult(a,mult(mult(b,c),b)),c) = mult(mult(a,b),mult(mult(c,b),c)) ),
% 1.40/1.78 file('/tmp/WALDMEISTER_9701_n025',conjecture_1)).
% 1.40/1.78 cnf('1.0.0.1',plain,
% 1.40/1.78 ( mult(mult(a,mult(b,mult(c,b))),c) = mult(mult(a,b),mult(mult(c,b),c)) ),
% 1.40/1.78 inference(reduction,[status(thm)],['1.0.0.0','0.7.2.0',theory(equality)]),
% 1.40/1.78 [pos('L.1.2','L')]).
% 1.40/1.78 cnf('1.0.0.2',plain,
% 1.40/1.78 ( mult(mult(a,mult(b,mult(c,b))),c) = mult(mult(a,b),mult(c,mult(b,c))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['1.0.0.1','0.7.2.0',theory(equality)]),
% 1.40/1.78 [pos('R.2','L')]).
% 1.40/1.78 cnf('1.0.0.3',plain,
% 1.40/1.78 ( mult(mult(a,mult(b,mult(c,b))),c) = mult(a,mult(b,mult(c,mult(b,c)))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['1.0.0.2','0.505.2.0',theory(equality)]),
% 1.40/1.78 [pos('R','L')]).
% 1.40/1.78 cnf('1.0.0.4',plain,
% 1.40/1.78 ( mult(a,mult(b,mult(c,mult(b,c)))) = mult(a,mult(b,mult(c,mult(b,c)))) ),
% 1.40/1.78 inference(reduction,[status(thm)],['1.0.0.3','0.620.2.0',theory(equality)]),
% 1.40/1.78 [pos('L','L')]).
% 1.40/1.78 cnf('1.0.0.5',plain,
% 1.40/1.78 ( $true ),
% 1.40/1.78 inference(trivial,[status(thm)],['1.0.0.4',theory(equality)]),
% 1.40/1.78 [conjecture_1]).
% 1.40/1.78
% 1.40/1.78 Proved Goals:
% 1.40/1.78 No. 1: mult(mult(a,mult(mult(b,c),b)),c) ?= mult(mult(a,b),mult(mult(c,b),c)) joined, current: mult(a,mult(b,mult(c,mult(b,c)))) = mult(a,mult(b,mult(c,mult(b,c))))
% 1.40/1.78 1 goal was specified, which was proved.
% 1.40/1.78 % SZS output end CNFRefutation
% 1.40/1.78 #END OF PROOF
% 1.40/1.78
% 1.40/1.78 Problem WALDMEISTER_9701_n025
% 1.40/1.78 CPs.gen 122176
% 1.40/1.78 CPs.reexp 0
% 1.40/1.78 Select 2526
% 1.40/1.78 R 620
% 1.40/1.78 E 0
% 1.40/1.78 vsize 6.6M
% 1.40/1.78 rss 4.1M
% 1.40/1.78 process.time 0.760s
% 1.40/1.78 wallclock.time 0.761s
% 1.40/1.78 status S
% 1.40/1.78
% 1.40/1.78
% 1.40/1.78 Waldmeister states: Goal proved.
% 1.40/1.78 % SZS status Unsatisfiable
%------------------------------------------------------------------------------