TSTP Solution File: GRP696-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP696-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:28:03 EDT 2022
% Result : Unsatisfiable 10.00s 10.38s
% Output : CNFRefutation 10.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP696-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n019.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 Jun 13 15:04:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.95 ********************************************************************************
% 0.55/0.95 * W A L D M E I S T E R \| \ / \|/ *
% 0.55/0.95 * |/ | \/ | *
% 0.55/0.95 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.55/0.95 * A. Jaeger and B. Loechner | | *
% 0.55/0.95 * <waldmeister@informatik.uni-kl.de> | *
% 0.55/0.95 ********************************************************************************
% 0.55/0.95
% 0.55/0.95
% 0.55/0.95 Goals:
% 0.55/0.95 ------
% 0.55/0.95
% 0.55/0.95 ( 1) mult(mult(mult(a,b),a),mult(a,c)) ?=? mult(a,mult(mult(mult(b,a),a),c))
% 0.55/0.95
% 0.55/0.95 Detected structure: Loop
% 0.55/0.95 ********************************************************************************
% 0.55/0.95 ****************************** COMPLETION - PROOF ******************************
% 0.55/0.95 ********************************************************************************
% 0.55/0.95
% 10.00/10.37 joined goal: 1 mult(mult(mult(a,b),a),mult(a,c)) ?= mult(a,mult(mult(mult(b,a),a),c)) to mult(a,mult(mult(mult(b,a),a),c))
% 10.00/10.37 goal joined
% 10.00/10.38 % SZS status Unsatisfiable
% 10.00/10.38 #START OF PROOF
% 10.00/10.38 % SZS output start CNFRefutation
% 10.00/10.38 cnf('0.1.0.0',axiom,
% 10.00/10.38 ( X1 = mult(X2,ld(X2,X1)) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.1.1.0',plain,
% 10.00/10.38 ( X1 = mult(X2,ld(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.1.0.0']),
% 10.00/10.38 [weight('<0,0,0,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.1.2.0',plain,
% 10.00/10.38 ( mult(X1,ld(X1,X2)) = X2 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_1]).
% 10.00/10.38 cnf('0.2.0.0',axiom,
% 10.00/10.38 ( X1 = mult(X1,unit) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.2.1.0',plain,
% 10.00/10.38 ( X1 = mult(X1,unit) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.2.0.0']),
% 10.00/10.38 [weight('<1,0,0,[0,0,0,2]>')]).
% 10.00/10.38 cnf('0.2.2.0',plain,
% 10.00/10.38 ( mult(X1,unit) = X1 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_2]).
% 10.00/10.38 cnf('0.3.0.0',axiom,
% 10.00/10.38 ( X1 = mult(unit,X1) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.3.1.0',plain,
% 10.00/10.38 ( X1 = mult(unit,X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.3.0.0']),
% 10.00/10.38 [weight('<2,0,0,[0,0,0,3]>')]).
% 10.00/10.38 cnf('0.3.2.0',plain,
% 10.00/10.38 ( mult(unit,X1) = X1 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_3]).
% 10.00/10.38 cnf('0.4.0.0',axiom,
% 10.00/10.38 ( X1 = mult(rd(X1,X2),X2) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.4.1.0',plain,
% 10.00/10.38 ( X1 = mult(rd(X1,X2),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.4.0.0']),
% 10.00/10.38 [weight('<3,0,0,[0,0,0,4]>')]).
% 10.00/10.38 cnf('0.4.2.0',plain,
% 10.00/10.38 ( mult(rd(X1,X2),X2) = X1 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_4]).
% 10.00/10.38 cnf('0.5.0.0',axiom,
% 10.00/10.38 ( X1 = rd(mult(X1,X2),X2) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.5.1.0',plain,
% 10.00/10.38 ( X1 = rd(mult(X1,X2),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.5.0.0']),
% 10.00/10.38 [weight('<4,0,0,[0,0,0,5]>')]).
% 10.00/10.38 cnf('0.5.2.0',plain,
% 10.00/10.38 ( rd(mult(X1,X2),X2) = X1 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_5]).
% 10.00/10.38 cnf('0.6.0.0',axiom,
% 10.00/10.38 ( X1 = ld(X2,mult(X2,X1)) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.6.1.0',plain,
% 10.00/10.38 ( X1 = ld(X2,mult(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.6.0.0']),
% 10.00/10.38 [weight('<5,0,0,[0,0,0,6]>')]).
% 10.00/10.38 cnf('0.6.2.0',plain,
% 10.00/10.38 ( ld(X1,mult(X1,X2)) = X2 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_6]).
% 10.00/10.38 cnf('0.7.0.0',axiom,
% 10.00/10.38 ( mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.7.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.7.0.0']),
% 10.00/10.38 [weight('<6,0,0,[0,0,0,7]>')]).
% 10.00/10.38 cnf('0.7.2.0',plain,
% 10.00/10.38 ( mult(rd(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(X2,X3)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_7]).
% 10.00/10.38 cnf('0.8.0.0',axiom,
% 10.00/10.38 ( mult(X1,i(X1)) = unit ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.8.1.0',plain,
% 10.00/10.38 ( mult(X1,i(X1)) = unit ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.8.0.0']),
% 10.00/10.38 [weight('<7,0,0,[0,0,0,8]>')]).
% 10.00/10.38 cnf('0.8.2.0',plain,
% 10.00/10.38 ( mult(X1,i(X1)) = unit ),
% 10.00/10.38 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_8]).
% 10.00/10.38 cnf('0.9.0.0',axiom,
% 10.00/10.38 ( mult(X1,i(mult(X2,X1))) = i(X2) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.9.1.0',plain,
% 10.00/10.38 ( mult(X1,i(mult(X2,X1))) = i(X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.9.0.0']),
% 10.00/10.38 [weight('<8,0,0,[0,0,0,9]>')]).
% 10.00/10.38 cnf('0.9.2.0',plain,
% 10.00/10.38 ( mult(X1,i(mult(X2,X1))) = i(X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_9]).
% 10.00/10.38 cnf('0.10.0.0',axiom,
% 10.00/10.38 ( mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.10.1.0',plain,
% 10.00/10.38 ( mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.10.0.0']),
% 10.00/10.38 [weight('<9,0,0,[0,0,0,10]>')]).
% 10.00/10.38 cnf('0.10.2.0',plain,
% 10.00/10.38 ( mult(mult(X1,X2),ld(X2,mult(X3,X2))) = mult(mult(X1,X3),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_10]).
% 10.00/10.38 cnf('0.11.0.0',axiom,
% 10.00/10.38 ( mult(i(X1),X1) = unit ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019')).
% 10.00/10.38 cnf('0.11.1.0',plain,
% 10.00/10.38 ( mult(i(X1),X1) = unit ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.11.0.0']),
% 10.00/10.38 [weight('<10,0,0,[0,0,0,11]>')]).
% 10.00/10.38 cnf('0.11.2.0',plain,
% 10.00/10.38 ( mult(i(X1),X1) = unit ),
% 10.00/10.38 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_11]).
% 10.00/10.38 cnf('0.16.0.0',plain,
% 10.00/10.38 ( unit = ld(X1,X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.16.1.0',plain,
% 10.00/10.38 ( unit = ld(X1,X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.16.0.0']),
% 10.00/10.38 [weight('<19,6,2,[1,0,0,2]>')]).
% 10.00/10.38 cnf('0.16.2.0',plain,
% 10.00/10.38 ( ld(X1,X1) = unit ),
% 10.00/10.38 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_16]).
% 10.00/10.38 cnf('0.18.0.0',plain,
% 10.00/10.38 ( i(X1) = rd(unit,X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.11.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.18.1.0',plain,
% 10.00/10.38 ( i(X1) = rd(unit,X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.18.0.0']),
% 10.00/10.38 [weight('<23,11,5,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.18.2.0',plain,
% 10.00/10.38 ( rd(unit,X1) = i(X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_18]).
% 10.00/10.38 cnf('0.19.0.0',plain,
% 10.00/10.38 ( X1 = rd(unit,i(X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.8.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.19.1.0',plain,
% 10.00/10.38 ( X1 = rd(unit,i(X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.19.0.0']),
% 10.00/10.38 [weight('<29,8,5,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.19.1.1',plain,
% 10.00/10.38 ( X1 = i(i(X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.19.1.0','0.18.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.19.2.0',plain,
% 10.00/10.38 ( i(i(X1)) = X1 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.19.1.1',theory(equality)]),
% 10.00/10.38 [x,rule_19]).
% 10.00/10.38 cnf('0.20.0.0',plain,
% 10.00/10.38 ( X1 = rd(X2,ld(X1,X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.20.1.0',plain,
% 10.00/10.38 ( X1 = rd(X2,ld(X1,X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.20.0.0']),
% 10.00/10.38 [weight('<41,5,1,[1,0,0,1]>')]).
% 10.00/10.38 cnf('0.20.2.0',plain,
% 10.00/10.38 ( rd(X1,ld(X2,X1)) = X2 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_20]).
% 10.00/10.38 cnf('0.21.0.0',plain,
% 10.00/10.38 ( X1 = ld(rd(X2,X1),X2) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.6.2.0','0.4.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.21.1.0',plain,
% 10.00/10.38 ( X1 = ld(rd(X2,X1),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.21.0.0']),
% 10.00/10.38 [weight('<41,6,4,[1,0,0,2]>')]).
% 10.00/10.38 cnf('0.21.2.0',plain,
% 10.00/10.38 ( ld(rd(X1,X2),X1) = X2 ),
% 10.00/10.38 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_21]).
% 10.00/10.38 cnf('0.22.0.0',plain,
% 10.00/10.38 ( i(rd(X1,X2)) = mult(X2,i(X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.9.2.0','0.4.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.1','L')]).
% 10.00/10.38 cnf('0.22.1.0',plain,
% 10.00/10.38 ( i(rd(X1,X2)) = mult(X2,i(X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.22.0.0']),
% 10.00/10.38 [weight('<44,9,4,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.22.2.0',plain,
% 10.00/10.38 ( i(rd(X1,X2)) = mult(X2,i(X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_22]).
% 10.00/10.38 cnf('0.23.0.0',plain,
% 10.00/10.38 ( i(mult(X1,X2)) = ld(X2,i(X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.6.2.0','0.9.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.23.1.0',plain,
% 10.00/10.38 ( i(mult(X1,X2)) = ld(X2,i(X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.23.0.0']),
% 10.00/10.38 [weight('<44,9,6,[0,0,0,2]>')]).
% 10.00/10.38 cnf('0.23.2.0',plain,
% 10.00/10.38 ( i(mult(X1,X2)) = ld(X2,i(X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_23]).
% 10.00/10.38 cnf('0.24.0.0',plain,
% 10.00/10.38 ( rd(X1,X2) = i(mult(X2,i(X1))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.19.2.0','0.22.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.24.1.0',plain,
% 10.00/10.38 ( rd(X1,X2) = i(mult(X2,i(X1))) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.24.0.0']),
% 10.00/10.38 [weight('<53,22,19,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.24.1.1',plain,
% 10.00/10.38 ( rd(X1,X2) = ld(i(X1),i(X2)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.24.1.0','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.24.2.0',plain,
% 10.00/10.38 ( ld(i(X1),i(X2)) = rd(X1,X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.24.1.1',theory(equality)]),
% 10.00/10.38 [x,rule_24]).
% 10.00/10.38 cnf('0.25.0.0',plain,
% 10.00/10.38 ( rd(i(X1),X2) = ld(X1,i(X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.24.2.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.25.1.0',plain,
% 10.00/10.38 ( rd(i(X1),X2) = ld(X1,i(X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.25.0.0']),
% 10.00/10.38 [weight('<44,24,19,[1,0,0,1]>')]).
% 10.00/10.38 cnf('0.25.2.0',plain,
% 10.00/10.38 ( rd(i(X1),X2) = ld(X1,i(X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_25]).
% 10.00/10.38 cnf('0.26.0.0',plain,
% 10.00/10.38 ( rd(X1,i(X2)) = ld(i(X1),X2) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.24.2.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.26.1.0',plain,
% 10.00/10.38 ( rd(X1,i(X2)) = ld(i(X1),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.26.0.0']),
% 10.00/10.38 [weight('<44,24,19,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.26.2.0',plain,
% 10.00/10.38 ( rd(X1,i(X2)) = ld(i(X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_26]).
% 10.00/10.38 cnf('0.27.0.0',plain,
% 10.00/10.38 ( mult(X1,X2) = i(ld(X2,i(X1))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.19.2.0','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.27.1.0',plain,
% 10.00/10.38 ( mult(X1,X2) = i(ld(X2,i(X1))) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.27.0.0']),
% 10.00/10.38 [weight('<53,23,19,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.27.2.0',plain,
% 10.00/10.38 ( i(ld(X1,i(X2))) = mult(X2,X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_27]).
% 10.00/10.38 cnf('0.28.0.0',plain,
% 10.00/10.38 ( mult(i(X1),X2) = i(ld(X2,X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.27.2.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.2','L')]).
% 10.00/10.38 cnf('0.28.1.0',plain,
% 10.00/10.38 ( mult(i(X1),X2) = i(ld(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.28.0.0']),
% 10.00/10.38 [weight('<44,27,19,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.28.2.0',plain,
% 10.00/10.38 ( i(ld(X1,X2)) = mult(i(X2),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_28]).
% 10.00/10.38 cnf('0.31.0.0',plain,
% 10.00/10.38 ( i(X1) = mult(i(X2),rd(X2,X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.1.2.0','0.24.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.31.1.0',plain,
% 10.00/10.38 ( i(X1) = mult(i(X2),rd(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.31.0.0']),
% 10.00/10.38 [weight('<62,24,1,[0,0,0,2]>')]).
% 10.00/10.38 cnf('0.31.2.0',plain,
% 10.00/10.38 ( mult(i(X1),rd(X1,X2)) = i(X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_31]).
% 10.00/10.38 cnf('0.34.0.0',plain,
% 10.00/10.38 ( mult(X1,mult(X2,i(X1))) = mult(rd(mult(X1,X2),X1),unit) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.7.2.0','0.8.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.34.0.1',plain,
% 10.00/10.38 ( mult(X1,mult(X2,i(X1))) = rd(mult(X1,X2),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.34.0.0','0.2.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.34.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(X2,i(X1))) = rd(mult(X1,X2),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.34.0.1']),
% 10.00/10.38 [weight('<83,8,7,[0,0,0,6]>')]).
% 10.00/10.38 cnf('0.34.2.0',plain,
% 10.00/10.38 ( mult(X1,mult(X2,i(X1))) = rd(mult(X1,X2),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_34]).
% 10.00/10.38 cnf('0.35.0.0',plain,
% 10.00/10.38 ( mult(mult(i(X1),X2),X1) = mult(unit,ld(X1,mult(X2,X1))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.10.2.0','0.11.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.35.0.1',plain,
% 10.00/10.38 ( mult(mult(i(X1),X2),X1) = ld(X1,mult(X2,X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.35.0.0','0.3.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.35.1.0',plain,
% 10.00/10.38 ( mult(mult(i(X1),X2),X1) = ld(X1,mult(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.35.0.1']),
% 10.00/10.38 [weight('<83,11,10,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.35.2.0',plain,
% 10.00/10.38 ( mult(mult(i(X1),X2),X1) = ld(X1,mult(X2,X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_35]).
% 10.00/10.38 cnf('0.36.0.0',plain,
% 10.00/10.38 ( rd(mult(i(X1),X2),i(X1)) = mult(i(X1),mult(X2,X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.34.2.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.2','L')]).
% 10.00/10.38 cnf('0.36.0.1',plain,
% 10.00/10.38 ( ld(i(mult(i(X1),X2)),X1) = mult(i(X1),mult(X2,X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.36.0.0','0.26.2.0',theory(equality)]),
% 10.00/10.38 [pos('L','L')]).
% 10.00/10.38 cnf('0.36.0.2',plain,
% 10.00/10.38 ( ld(ld(X2,i(i(X1))),X1) = mult(i(X1),mult(X2,X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.36.0.1','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.36.0.3',plain,
% 10.00/10.38 ( ld(ld(X2,X1),X1) = mult(i(X1),mult(X2,X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.36.0.2','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.2','L')]).
% 10.00/10.38 cnf('0.36.1.0',plain,
% 10.00/10.38 ( ld(ld(X2,X1),X1) = mult(i(X1),mult(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.36.0.3']),
% 10.00/10.38 [weight('<83,34,19,[1,0,0,4]>')]).
% 10.00/10.38 cnf('0.36.2.0',plain,
% 10.00/10.38 ( mult(i(X1),mult(X2,X1)) = ld(ld(X2,X1),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_36]).
% 10.00/10.38 cnf('0.37.0.0',plain,
% 10.00/10.38 ( ld(X1,i(mult(i(X1),X2))) = i(ld(X1,mult(X2,X1))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.23.2.0','0.35.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.37.0.1',plain,
% 10.00/10.38 ( ld(X1,ld(X2,i(i(X1)))) = i(ld(X1,mult(X2,X1))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.37.0.0','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.37.0.2',plain,
% 10.00/10.38 ( ld(X1,ld(X2,X1)) = i(ld(X1,mult(X2,X1))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.37.0.1','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.2','L')]).
% 10.00/10.38 cnf('0.37.0.3',plain,
% 10.00/10.38 ( ld(X1,ld(X2,X1)) = mult(i(mult(X2,X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.37.0.2','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.37.0.4',plain,
% 10.00/10.38 ( ld(X1,ld(X2,X1)) = mult(ld(X1,i(X2)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.37.0.3','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.37.1.0',plain,
% 10.00/10.38 ( ld(X1,ld(X2,X1)) = mult(ld(X1,i(X2)),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.37.0.4']),
% 10.00/10.38 [weight('<83,35,23,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.37.2.0',plain,
% 10.00/10.38 ( mult(ld(X1,i(X2)),X1) = ld(X1,ld(X2,X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_37]).
% 10.00/10.38 cnf('0.38.0.0',plain,
% 10.00/10.38 ( ld(i(X1),ld(X1,i(X1))) = mult(unit,i(X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.37.2.0','0.16.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.38.0.1',plain,
% 10.00/10.38 ( ld(i(X1),ld(X1,i(X1))) = i(X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.38.0.0','0.3.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.38.1.0',plain,
% 10.00/10.38 ( ld(i(X1),ld(X1,i(X1))) = i(X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.38.0.1']),
% 10.00/10.38 [weight('<79,37,16,[1,0,0,1]>')]).
% 10.00/10.38 cnf('0.38.2.0',plain,
% 10.00/10.38 ( ld(i(X1),ld(X1,i(X1))) = i(X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_38]).
% 10.00/10.38 cnf('0.40.0.0',plain,
% 10.00/10.38 ( i(X1) = rd(ld(X1,i(X1)),i(X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.20.2.0','0.38.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.40.0.1',plain,
% 10.00/10.38 ( i(X1) = ld(i(ld(X1,i(X1))),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.40.0.0','0.26.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.40.0.2',plain,
% 10.00/10.38 ( i(X1) = ld(mult(i(i(X1)),X1),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.40.0.1','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.40.0.3',plain,
% 10.00/10.38 ( i(X1) = ld(mult(X1,X1),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.40.0.2','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1.1','L')]).
% 10.00/10.38 cnf('0.40.1.0',plain,
% 10.00/10.38 ( i(X1) = ld(mult(X1,X1),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.40.0.3']),
% 10.00/10.38 [weight('<47,38,20,[0,0,0,2]>')]).
% 10.00/10.38 cnf('0.40.2.0',plain,
% 10.00/10.38 ( ld(mult(X1,X1),X1) = i(X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_40]).
% 10.00/10.38 cnf('0.44.0.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),i(i(X2))) = i(ld(ld(X1,X2),X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.23.2.0','0.36.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.44.0.1',plain,
% 10.00/10.38 ( ld(mult(X1,X2),X2) = i(ld(ld(X1,X2),X2)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.44.0.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.44.0.2',plain,
% 10.00/10.38 ( ld(mult(X1,X2),X2) = mult(i(X2),ld(X1,X2)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.44.0.1','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.44.1.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),X2) = mult(i(X2),ld(X1,X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.44.0.2']),
% 10.00/10.38 [weight('<83,36,23,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.44.2.0',plain,
% 10.00/10.38 ( mult(i(X1),ld(X2,X1)) = ld(mult(X2,X1),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_44]).
% 10.00/10.38 cnf('0.55.0.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),i(X3)) = rd(ld(X2,i(X1)),X3) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.25.2.0','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.55.1.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),i(X3)) = rd(ld(X2,i(X1)),X3) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.55.0.0']),
% 10.00/10.38 [weight('<90,25,23,[1,0,0,1]>')]).
% 10.00/10.38 cnf('0.55.2.0',plain,
% 10.00/10.38 ( rd(ld(X1,i(X2)),X3) = ld(mult(X2,X1),i(X3)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_55]).
% 10.00/10.38 cnf('0.57.0.0',plain,
% 10.00/10.38 ( ld(i(X1),mult(X2,X3)) = rd(X1,ld(X3,i(X2))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.26.2.0','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.57.1.0',plain,
% 10.00/10.38 ( ld(i(X1),mult(X2,X3)) = rd(X1,ld(X3,i(X2))) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.57.0.0']),
% 10.00/10.38 [weight('<90,26,23,[1,0,0,2]>')]).
% 10.00/10.38 cnf('0.57.2.0',plain,
% 10.00/10.38 ( rd(X1,ld(X2,i(X3))) = ld(i(X1),mult(X3,X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_57]).
% 10.00/10.38 cnf('0.58.0.0',plain,
% 10.00/10.38 ( ld(ld(X1,X2),i(X3)) = rd(mult(i(X2),X1),X3) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.25.2.0','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.58.1.0',plain,
% 10.00/10.38 ( ld(ld(X1,X2),i(X3)) = rd(mult(i(X2),X1),X3) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.58.0.0']),
% 10.00/10.38 [weight('<90,28,25,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.58.2.0',plain,
% 10.00/10.38 ( rd(mult(i(X1),X2),X3) = ld(ld(X2,X1),i(X3)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_58]).
% 10.00/10.38 cnf('0.62.0.0',plain,
% 10.00/10.38 ( mult(X1,i(X2)) = ld(X2,rd(mult(X2,X1),X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.6.2.0','0.34.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.62.1.0',plain,
% 10.00/10.38 ( mult(X1,i(X2)) = ld(X2,rd(mult(X2,X1),X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.62.0.0']),
% 10.00/10.38 [weight('<95,34,6,[0,0,0,2]>')]).
% 10.00/10.38 cnf('0.62.2.0',plain,
% 10.00/10.38 ( ld(X1,rd(mult(X1,X2),X1)) = mult(X2,i(X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_62]).
% 10.00/10.38 cnf('0.63.0.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),i(X1)) = ld(X1,rd(X2,X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.62.2.0','0.1.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.1','L')]).
% 10.00/10.38 cnf('0.63.1.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),i(X1)) = ld(X1,rd(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.63.0.0']),
% 10.00/10.38 [weight('<83,62,1,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.63.2.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),i(X1)) = ld(X1,rd(X2,X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_63]).
% 10.00/10.38 cnf('0.64.0.0',plain,
% 10.00/10.38 ( mult(rd(X1,X2),i(i(X1))) = ld(i(X1),rd(i(X2),i(X1))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.62.2.0','0.31.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.1','L')]).
% 10.00/10.38 cnf('0.64.0.1',plain,
% 10.00/10.38 ( mult(rd(X1,X2),X1) = ld(i(X1),rd(i(X2),i(X1))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.64.0.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.64.0.2',plain,
% 10.00/10.38 ( mult(rd(X1,X2),X1) = ld(i(X1),ld(X2,i(i(X1)))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.64.0.1','0.25.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.2','L')]).
% 10.00/10.38 cnf('0.64.0.3',plain,
% 10.00/10.38 ( mult(rd(X1,X2),X1) = ld(i(X1),ld(X2,X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.64.0.2','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.2.2','L')]).
% 10.00/10.38 cnf('0.64.1.0',plain,
% 10.00/10.38 ( mult(rd(X1,X2),X1) = ld(i(X1),ld(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.64.0.3']),
% 10.00/10.38 [weight('<83,62,31,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.64.2.0',plain,
% 10.00/10.38 ( ld(i(X1),ld(X2,X1)) = mult(rd(X1,X2),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_64]).
% 10.00/10.38 cnf('0.65.0.0',plain,
% 10.00/10.38 ( ld(i(X1),i(ld(X1,X2))) = i(ld(X1,rd(X2,X1))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.23.2.0','0.63.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.65.0.1',plain,
% 10.00/10.38 ( rd(X1,ld(X1,X2)) = i(ld(X1,rd(X2,X1))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.65.0.0','0.24.2.0',theory(equality)]),
% 10.00/10.38 [pos('L','L')]).
% 10.00/10.38 cnf('0.65.0.2',plain,
% 10.00/10.38 ( rd(X1,ld(X1,X2)) = mult(i(rd(X2,X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.65.0.1','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.65.0.3',plain,
% 10.00/10.38 ( rd(X1,ld(X1,X2)) = mult(mult(X1,i(X2)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.65.0.2','0.22.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.65.1.0',plain,
% 10.00/10.38 ( rd(X1,ld(X1,X2)) = mult(mult(X1,i(X2)),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.65.0.3']),
% 10.00/10.38 [weight('<83,63,23,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.65.2.0',plain,
% 10.00/10.38 ( mult(mult(X1,i(X2)),X1) = rd(X1,ld(X1,X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_65]).
% 10.00/10.38 cnf('0.68.0.0',plain,
% 10.00/10.38 ( mult(rd(mult(X1,X2),X1),mult(X1,X2)) = ld(i(mult(X1,X2)),X2) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.64.2.0','0.6.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.68.0.1',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X2)) = ld(i(mult(X1,X2)),X2) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.68.0.0','0.7.2.0',theory(equality)]),
% 10.00/10.38 [pos('L','L')]).
% 10.00/10.38 cnf('0.68.0.2',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X2)) = ld(ld(X2,i(X1)),X2) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.68.0.1','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.68.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X2)) = ld(ld(X2,i(X1)),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.68.0.2']),
% 10.00/10.38 [weight('<83,64,6,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.68.2.0',plain,
% 10.00/10.38 ( ld(ld(X1,i(X2)),X1) = mult(X2,mult(X1,X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_68]).
% 10.00/10.38 cnf('0.69.0.0',plain,
% 10.00/10.38 ( rd(X1,ld(X1,i(X2))) = mult(mult(X1,X2),X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.65.2.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.2','L')]).
% 10.00/10.38 cnf('0.69.0.1',plain,
% 10.00/10.38 ( ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.69.0.0','0.57.2.0',theory(equality)]),
% 10.00/10.38 [pos('L','L')]).
% 10.00/10.38 cnf('0.69.1.0',plain,
% 10.00/10.38 ( ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.69.0.1']),
% 10.00/10.38 [weight('<83,65,19,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.69.2.0',plain,
% 10.00/10.38 ( ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_69]).
% 10.00/10.38 cnf('0.70.0.0',plain,
% 10.00/10.38 ( mult(i(X1),mult(X2,X2)) = ld(ld(X2,X1),X2) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.68.2.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.2','L')]).
% 10.00/10.38 cnf('0.70.1.0',plain,
% 10.00/10.38 ( mult(i(X1),mult(X2,X2)) = ld(ld(X2,X1),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.70.0.0']),
% 10.00/10.38 [weight('<83,68,19,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.70.2.0',plain,
% 10.00/10.38 ( mult(i(X1),mult(X2,X2)) = ld(ld(X2,X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_70]).
% 10.00/10.38 cnf('0.71.0.0',plain,
% 10.00/10.38 ( ld(mult(X1,X1),i(i(X2))) = i(ld(ld(X1,X2),X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.23.2.0','0.70.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.71.0.1',plain,
% 10.00/10.38 ( ld(mult(X1,X1),X2) = i(ld(ld(X1,X2),X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.71.0.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.71.0.2',plain,
% 10.00/10.38 ( ld(mult(X1,X1),X2) = mult(i(X1),ld(X1,X2)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.71.0.1','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.71.1.0',plain,
% 10.00/10.38 ( ld(mult(X1,X1),X2) = mult(i(X1),ld(X1,X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.71.0.2']),
% 10.00/10.38 [weight('<83,70,23,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.71.2.0',plain,
% 10.00/10.38 ( mult(i(X1),ld(X1,X2)) = ld(mult(X1,X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_71]).
% 10.00/10.38 cnf('0.72.0.0',plain,
% 10.00/10.38 ( mult(X1,X2) = mult(i(X2),mult(mult(X2,X1),X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.1.2.0','0.69.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.72.0.1',plain,
% 10.00/10.38 ( mult(X1,X2) = ld(ld(mult(X2,X1),X2),X2) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.72.0.0','0.36.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.72.1.0',plain,
% 10.00/10.38 ( mult(X1,X2) = ld(ld(mult(X2,X1),X2),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.72.0.1']),
% 10.00/10.38 [weight('<87,69,1,[0,0,0,2]>')]).
% 10.00/10.38 cnf('0.72.2.0',plain,
% 10.00/10.38 ( ld(ld(mult(X1,X2),X1),X1) = mult(X2,X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.72.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_72]).
% 10.00/10.38 cnf('0.73.0.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),X1) = ld(ld(X2,X1),X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.72.2.0','0.1.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.1','L')]).
% 10.00/10.38 cnf('0.73.1.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),X1) = ld(ld(X2,X1),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.73.0.0']),
% 10.00/10.38 [weight('<65,72,1,[1,0,0,2]>')]).
% 10.00/10.38 cnf('0.73.2.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),X1) = ld(ld(X2,X1),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_73]).
% 10.00/10.38 cnf('0.75.0.0',plain,
% 10.00/10.38 ( ld(ld(ld(X1,X2),X1),X1) = mult(i(X1),ld(ld(X2,X1),X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.36.2.0','0.73.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.75.0.1',plain,
% 10.00/10.38 ( ld(ld(ld(X1,X2),X1),X1) = ld(mult(ld(X2,X1),X1),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.75.0.0','0.44.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.75.1.0',plain,
% 10.00/10.38 ( ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.75.0.1']),
% 10.00/10.38 [weight('<65,73,36,[0,0,0,3]>')]).
% 10.00/10.38 cnf('0.75.2.0',plain,
% 10.00/10.38 ( mult(ld(X1,X2),X2) = ld(ld(X2,X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_75]).
% 10.00/10.38 cnf('0.76.0.0',plain,
% 10.00/10.38 ( mult(mult(X1,ld(X2,X1)),X1) = ld(i(X1),ld(ld(X1,X2),X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.69.2.0','0.75.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.76.0.1',plain,
% 10.00/10.38 ( mult(mult(X1,ld(X2,X1)),X1) = mult(rd(X1,ld(X1,X2)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.76.0.0','0.64.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.76.1.0',plain,
% 10.00/10.38 ( mult(X1,ld(X2,X1)) = rd(X1,ld(X1,X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.76.0.1']),
% 10.00/10.38 [weight('<65,75,69,[0,0,0,3]>')]).
% 10.00/10.38 cnf('0.76.2.0',plain,
% 10.00/10.38 ( mult(X1,ld(X2,X1)) = rd(X1,ld(X1,X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_76]).
% 10.00/10.38 cnf('0.80.0.0',plain,
% 10.00/10.38 ( ld(X1,i(ld(X2,X1))) = i(ld(ld(X1,X2),X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.23.2.0','0.75.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.80.0.1',plain,
% 10.00/10.38 ( ld(X1,mult(i(X1),X2)) = i(ld(ld(X1,X2),X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.80.0.0','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.80.0.2',plain,
% 10.00/10.38 ( ld(X1,mult(i(X1),X2)) = mult(i(X1),ld(X1,X2)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.80.0.1','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.80.0.3',plain,
% 10.00/10.38 ( ld(X1,mult(i(X1),X2)) = ld(mult(X1,X1),X2) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.80.0.2','0.71.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.80.1.0',plain,
% 10.00/10.38 ( ld(X1,mult(i(X1),X2)) = ld(mult(X1,X1),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.80.0.3']),
% 10.00/10.38 [weight('<83,75,23,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.80.2.0',plain,
% 10.00/10.38 ( ld(X1,mult(i(X1),X2)) = ld(mult(X1,X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.80.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_80]).
% 10.00/10.38 cnf('0.85.0.0',plain,
% 10.00/10.38 ( ld(X1,X2) = rd(ld(ld(X2,X1),X1),X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.73.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.85.1.0',plain,
% 10.00/10.38 ( ld(X1,X2) = rd(ld(ld(X2,X1),X1),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.85.0.0']),
% 10.00/10.38 [weight('<87,73,5,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.85.2.0',plain,
% 10.00/10.38 ( rd(ld(ld(X1,X2),X2),X2) = ld(X2,X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.85.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_85]).
% 10.00/10.38 cnf('0.86.0.0',plain,
% 10.00/10.38 ( ld(X1,rd(X1,X2)) = rd(ld(X2,X1),X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.85.2.0','0.21.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.1','L')]).
% 10.00/10.38 cnf('0.86.1.0',plain,
% 10.00/10.38 ( ld(X1,rd(X1,X2)) = rd(ld(X2,X1),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.86.0.0']),
% 10.00/10.38 [weight('<65,85,21,[1,0,0,2]>')]).
% 10.00/10.38 cnf('0.86.2.0',plain,
% 10.00/10.38 ( rd(ld(X1,X2),X2) = ld(X2,rd(X2,X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.86.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_86]).
% 10.00/10.38 cnf('0.89.0.0',plain,
% 10.00/10.38 ( ld(X1,X2) = rd(ld(ld(X2,X1),X2),X2) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.75.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.89.1.0',plain,
% 10.00/10.38 ( ld(X1,X2) = rd(ld(ld(X2,X1),X2),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.89.0.0']),
% 10.00/10.38 [weight('<87,75,5,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.89.1.1',plain,
% 10.00/10.38 ( ld(X1,X2) = ld(X2,rd(X2,ld(X2,X1))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.89.1.0','0.86.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.89.2.0',plain,
% 10.00/10.38 ( ld(X1,rd(X1,ld(X1,X2))) = ld(X2,X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.89.1.1',theory(equality)]),
% 10.00/10.38 [x,rule_89]).
% 10.00/10.38 cnf('0.90.0.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),X1) = ld(X1,rd(X1,X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.89.2.0','0.6.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.2','L')]).
% 10.00/10.38 cnf('0.90.1.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),X1) = ld(X1,rd(X1,X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.90.0.0']),
% 10.00/10.38 [weight('<65,89,6,[1,0,0,4]>')]).
% 10.00/10.38 cnf('0.90.2.0',plain,
% 10.00/10.38 ( ld(mult(X1,X2),X1) = ld(X1,rd(X1,X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.90.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_90]).
% 10.00/10.38 cnf('0.105.0.0',plain,
% 10.00/10.38 ( ld(ld(ld(X1,i(X2)),X2),i(X3)) = rd(rd(i(X2),ld(i(X2),X1)),X3) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.58.2.0','0.76.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.105.0.1',plain,
% 10.00/10.38 ( ld(ld(ld(X1,i(X2)),X2),i(X3)) = rd(ld(X2,i(ld(i(X2),X1))),X3) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.105.0.0','0.25.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.105.0.2',plain,
% 10.00/10.38 ( ld(ld(ld(X1,i(X2)),X2),i(X3)) = ld(mult(ld(i(X2),X1),X2),i(X3)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.105.0.1','0.55.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.105.1.0',plain,
% 10.00/10.38 ( ld(ld(X1,i(X2)),X2) = mult(ld(i(X2),X1),X2) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.105.0.2']),
% 10.00/10.38 [weight('<90,76,58,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.105.2.0',plain,
% 10.00/10.38 ( mult(ld(i(X1),X2),X1) = ld(ld(X2,i(X1)),X1) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.105.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_105]).
% 10.00/10.38 cnf('0.106.0.0',plain,
% 10.00/10.38 ( mult(mult(X1,i(X2)),X2) = mult(mult(X1,X2),ld(mult(X2,X2),X2)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.10.2.0','0.80.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.106.0.1',plain,
% 10.00/10.38 ( mult(mult(X1,i(X2)),X2) = mult(mult(X1,X2),i(X2)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.106.0.0','0.40.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.2','L')]).
% 10.00/10.38 cnf('0.106.1.0',plain,
% 10.00/10.38 ( mult(mult(X1,i(X2)),X2) = mult(mult(X1,X2),i(X2)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.106.0.1']),
% 10.00/10.38 [weight('<90,80,10,[0,0,0,4]>')]).
% 10.00/10.38 cnf('0.106.2.0',plain,
% 10.00/10.38 ( mult(mult(X1,i(X2)),X2) = mult(mult(X1,X2),i(X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_106]).
% 10.00/10.38 cnf('0.107.0.0',plain,
% 10.00/10.38 ( mult(X1,i(ld(X2,X1))) = i(ld(X1,rd(X1,X2))) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.22.2.0','0.86.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.107.0.1',plain,
% 10.00/10.38 ( mult(X1,mult(i(X1),X2)) = i(ld(X1,rd(X1,X2))) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.107.0.0','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2','L')]).
% 10.00/10.38 cnf('0.107.0.2',plain,
% 10.00/10.38 ( mult(X1,mult(i(X1),X2)) = mult(i(rd(X1,X2)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.107.0.1','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.107.0.3',plain,
% 10.00/10.38 ( mult(X1,mult(i(X1),X2)) = mult(mult(X2,i(X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.107.0.2','0.22.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.107.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(i(X1),X2)) = mult(mult(X2,i(X1)),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.107.0.3']),
% 10.00/10.38 [weight('<90,86,22,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.107.1.1',plain,
% 10.00/10.38 ( mult(X1,mult(i(X1),X2)) = mult(mult(X2,X1),i(X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.107.1.0','0.106.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.107.2.0',plain,
% 10.00/10.38 ( mult(mult(X1,X2),i(X2)) = mult(X2,mult(i(X2),X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.107.1.1',theory(equality)]),
% 10.00/10.38 [x,rule_107]).
% 10.00/10.38 cnf('0.108.0.0',plain,
% 10.00/10.38 ( mult(X1,mult(ld(X1,X2),X3)) = mult(rd(X2,X1),mult(X1,X3)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.7.2.0','0.1.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.1','L')]).
% 10.00/10.38 cnf('0.108.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(ld(X1,X2),X3)) = mult(rd(X2,X1),mult(X1,X3)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.108.0.0']),
% 10.00/10.38 [weight('<?,7,1,[1,0,0,2]>')]).
% 10.00/10.38 cnf('0.108.2.0',plain,
% 10.00/10.38 ( mult(rd(X1,X2),mult(X2,X3)) = mult(X2,mult(ld(X2,X1),X3)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_108]).
% 10.00/10.38 cnf('0.117.0.0',plain,
% 10.00/10.38 ( mult(i(X1),X2) = rd(ld(X1,mult(X2,X1)),X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.35.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.117.1.0',plain,
% 10.00/10.38 ( mult(i(X1),X2) = rd(ld(X1,mult(X2,X1)),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.117.0.0']),
% 10.00/10.38 [weight('<95,35,5,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.117.2.0',plain,
% 10.00/10.38 ( rd(ld(X1,mult(X2,X1)),X1) = mult(i(X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.117.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_117]).
% 10.00/10.38 cnf('0.121.0.0',plain,
% 10.00/10.38 ( mult(i(i(X1)),mult(X2,X1)) = rd(ld(i(X1),mult(X1,mult(i(X1),X2))),i(X1)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.117.2.0','0.107.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1.2','L')]).
% 10.00/10.38 cnf('0.121.0.1',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = rd(ld(i(X1),mult(X1,mult(i(X1),X2))),i(X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.0','0.19.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.121.0.2',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(i(ld(i(X1),mult(X1,mult(i(X1),X2)))),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.1','0.26.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.121.0.3',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(mult(i(mult(X1,mult(i(X1),X2))),i(X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.2','0.28.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.121.0.4',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(mult(ld(mult(i(X1),X2),i(X1)),i(X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.3','0.23.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1.1','L')]).
% 10.00/10.38 cnf('0.121.0.5',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(mult(ld(i(X1),rd(i(X1),X2)),i(X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.4','0.90.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1.1','L')]).
% 10.00/10.38 cnf('0.121.0.6',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(ld(ld(rd(i(X1),X2),i(X1)),i(X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.5','0.73.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1','L')]).
% 10.00/10.38 cnf('0.121.0.7',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(ld(X2,i(X1)),X1) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.121.0.6','0.21.2.0',theory(equality)]),
% 10.00/10.38 [pos('R.1.1','L')]).
% 10.00/10.38 cnf('0.121.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(X2,X1)) = ld(ld(X2,i(X1)),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.121.0.7']),
% 10.00/10.38 [weight('<83,117,107,[1,0,0,3]>')]).
% 10.00/10.38 cnf('0.121.2.0',plain,
% 10.00/10.38 ( ld(ld(X1,i(X2)),X2) = mult(X2,mult(X1,X2)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.121.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_121]).
% 10.00/10.38 cnf('0.122.0.0',plain,
% 10.00/10.38 ( mult(ld(i(X1),X2),X1) = ld(ld(X2,i(X1)),X1) ),
% 10.00/10.38 inference(interreduction_right,[status(thm)],['0.105.2.0'])).
% 10.00/10.38 cnf('0.122.0.1',plain,
% 10.00/10.38 ( mult(ld(i(X1),X2),X1) = mult(X1,mult(X2,X1)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.122.0.0','0.121.2.0',theory(equality)]),
% 10.00/10.38 [pos('R','L')]).
% 10.00/10.38 cnf('0.122.1.0',plain,
% 10.00/10.38 ( mult(ld(i(X1),X2),X1) = mult(X1,mult(X2,X1)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.122.0.1']),
% 10.00/10.38 [weight('<83,105,121,[0,0,0,0]>')]).
% 10.00/10.38 cnf('0.122.2.0',plain,
% 10.00/10.38 ( mult(ld(i(X1),X2),X1) = mult(X1,mult(X2,X1)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.122.1.0',theory(equality)]),
% 10.00/10.38 [u,rule_122]).
% 10.00/10.38 cnf('0.148.0.0',plain,
% 10.00/10.38 ( ld(i(X1),X2) = rd(mult(X1,mult(X2,X1)),X1) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.5.2.0','0.122.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.148.1.0',plain,
% 10.00/10.38 ( ld(i(X1),X2) = rd(mult(X1,mult(X2,X1)),X1) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.148.0.0']),
% 10.00/10.38 [weight('<95,122,5,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.148.2.0',plain,
% 10.00/10.38 ( rd(mult(X1,mult(X2,X1)),X1) = ld(i(X1),X2) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.148.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_148]).
% 10.00/10.38 cnf('0.454.0.0',plain,
% 10.00/10.38 ( mult(X1,mult(ld(X1,mult(X1,mult(X2,X1))),X3)) = mult(ld(i(X1),X2),mult(X1,X3)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.108.2.0','0.148.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.454.0.1',plain,
% 10.00/10.38 ( mult(X1,mult(mult(X2,X1),X3)) = mult(ld(i(X1),X2),mult(X1,X3)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['0.454.0.0','0.6.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.2.1','L')]).
% 10.00/10.38 cnf('0.454.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(mult(X2,X1),X3)) = mult(ld(i(X1),X2),mult(X1,X3)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.454.0.1']),
% 10.00/10.38 [weight('<143,148,108,[0,0,0,1]>')]).
% 10.00/10.38 cnf('0.454.2.0',plain,
% 10.00/10.38 ( mult(ld(i(X1),X2),mult(X1,X3)) = mult(X1,mult(mult(X2,X1),X3)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.454.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_454]).
% 10.00/10.38 cnf('0.2222.0.0',plain,
% 10.00/10.38 ( mult(X1,mult(mult(mult(X2,X1),X1),X3)) = mult(mult(mult(X1,X2),X1),mult(X1,X3)) ),
% 10.00/10.38 inference(cp,[status(thm)],['0.454.2.0','0.69.2.0',theory(equality)]),
% 10.00/10.38 [pos('L.1','L')]).
% 10.00/10.38 cnf('0.2222.1.0',plain,
% 10.00/10.38 ( mult(X1,mult(mult(mult(X2,X1),X1),X3)) = mult(mult(mult(X1,X2),X1),mult(X1,X3)) ),
% 10.00/10.38 inference(weigh,[status(thm)],['0.2222.0.0']),
% 10.00/10.38 [weight('<189,454,69,[1,0,0,1]>')]).
% 10.00/10.38 cnf('0.2222.2.0',plain,
% 10.00/10.38 ( mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)) ),
% 10.00/10.38 inference(orient,[status(thm)],['0.2222.1.0',theory(equality)]),
% 10.00/10.38 [x,rule_2219]).
% 10.00/10.38 cnf('1.0.0.0',conjecture,
% 10.00/10.38 ( mult(mult(mult(a,b),a),mult(a,c)) = mult(a,mult(mult(mult(b,a),a),c)) ),
% 10.00/10.38 file('/tmp/WALDMEISTER_22750_n019',conjecture_1)).
% 10.00/10.38 cnf('1.0.0.1',plain,
% 10.00/10.38 ( mult(a,mult(mult(mult(b,a),a),c)) = mult(a,mult(mult(mult(b,a),a),c)) ),
% 10.00/10.38 inference(reduction,[status(thm)],['1.0.0.0','0.2222.2.0',theory(equality)]),
% 10.00/10.38 [pos('L','L')]).
% 10.00/10.38 cnf('1.0.0.2',plain,
% 10.00/10.38 ( $true ),
% 10.00/10.38 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 10.00/10.38 [conjecture_1]).
% 10.00/10.38
% 10.00/10.38 Proved Goals:
% 10.00/10.38 No. 1: mult(mult(mult(a,b),a),mult(a,c)) ?= mult(a,mult(mult(mult(b,a),a),c)) joined, current: mult(a,mult(mult(mult(b,a),a),c)) = mult(a,mult(mult(mult(b,a),a),c))
% 10.00/10.38 1 goal was specified, which was proved.
% 10.00/10.38 % SZS output end CNFRefutation
% 10.00/10.38 #END OF PROOF
% 10.00/10.38
% 10.00/10.38 Problem WALDMEISTER_22750_n019
% 10.00/10.38 CPs.gen 1531898
% 10.00/10.38 CPs.reexp 0
% 10.00/10.38 Select 18046
% 10.00/10.38 R 2219
% 10.00/10.38 E 3
% 10.00/10.38 vsize 9.8M
% 10.00/10.38 rss 5.3M
% 10.00/10.38 process.time 9.425s
% 10.00/10.38 wallclock.time 9.426s
% 10.00/10.38 status S
% 10.00/10.38
% 10.00/10.38
% 10.00/10.38 Waldmeister states: Goal proved.
% 10.00/10.38 % SZS status Unsatisfiable
%------------------------------------------------------------------------------