TSTP Solution File: GRP777-10 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP777-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n011.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 12:28:30 EDT 2022
% Result : Unsatisfiable 0.81s 1.19s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP777-10 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n011.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 : Tue Jun 14 04:02:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.67/1.06 ********************************************************************************
% 0.67/1.06 * W A L D M E I S T E R \| \ / \|/ *
% 0.67/1.06 * |/ | \/ | *
% 0.67/1.06 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.67/1.06 * A. Jaeger and B. Loechner | | *
% 0.67/1.06 * <waldmeister@informatik.uni-kl.de> | *
% 0.67/1.06 ********************************************************************************
% 0.67/1.06
% 0.67/1.06
% 0.67/1.06 Goals:
% 0.67/1.06 ------
% 0.67/1.06
% 0.67/1.06 ( 1) bigC(a,b,x0) ?=? bigC(c,c,x0)
% 0.67/1.06
% 0.67/1.06 Detected structure: Quasigruppe
% 0.67/1.06 ********************************************************************************
% 0.67/1.06 ****************************** COMPLETION - PROOF ******************************
% 0.67/1.06 ********************************************************************************
% 0.67/1.06
% 0.81/1.19 joined goal: 1 bigC(a,b,x0) ?= bigC(c,c,x0) to bigC(c,c,x0)
% 0.81/1.19 goal joined
% 0.81/1.19 % SZS status Unsatisfiable
% 0.81/1.19 #START OF PROOF
% 0.81/1.19 % SZS output start CNFRefutation
% 0.81/1.19 cnf('0.1.0.0',axiom,
% 0.81/1.19 ( X1 = product(X2,difference(X2,X1)) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.1.1.0',plain,
% 0.81/1.19 ( X1 = product(X2,difference(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.81/1.19 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.1.2.0',plain,
% 0.81/1.19 ( product(X1,difference(X1,X2)) = X2 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_1]).
% 0.81/1.19 cnf('0.2.0.0',axiom,
% 0.81/1.19 ( X1 = product(X1,X1) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.2.1.0',plain,
% 0.81/1.19 ( X1 = product(X1,X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.81/1.19 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.2.2.0',plain,
% 0.81/1.19 ( product(X1,X1) = X1 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_2]).
% 0.81/1.19 cnf('0.3.0.0',axiom,
% 0.81/1.19 ( X1 = product(product(product(X2,X1),X1),product(X1,product(X1,X2))) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.3.1.0',plain,
% 0.81/1.19 ( X1 = product(product(product(X2,X1),X1),product(X1,product(X1,X2))) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.81/1.19 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.81/1.19 cnf('0.3.2.0',plain,
% 0.81/1.19 ( product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_3]).
% 0.81/1.19 cnf('0.4.0.0',axiom,
% 0.81/1.19 ( X1 = product(quotient(X1,X2),X2) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.4.1.0',plain,
% 0.81/1.19 ( X1 = product(quotient(X1,X2),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.81/1.19 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.81/1.19 cnf('0.4.2.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),X2) = X1 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_4]).
% 0.81/1.19 cnf('0.5.0.0',axiom,
% 0.81/1.19 ( X1 = quotient(product(X1,X2),X2) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.5.1.0',plain,
% 0.81/1.19 ( X1 = quotient(product(X1,X2),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.81/1.19 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.81/1.19 cnf('0.5.2.0',plain,
% 0.81/1.19 ( quotient(product(X1,X2),X2) = X1 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_5]).
% 0.81/1.19 cnf('0.6.0.0',axiom,
% 0.81/1.19 ( X1 = difference(X2,product(X2,X1)) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.6.1.0',plain,
% 0.81/1.19 ( X1 = difference(X2,product(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.81/1.19 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.81/1.19 cnf('0.6.2.0',plain,
% 0.81/1.19 ( difference(X1,product(X1,X2)) = X2 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_6]).
% 0.81/1.19 cnf('0.7.0.0',axiom,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.7.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.81/1.19 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.81/1.19 cnf('0.7.2.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)) ),
% 0.81/1.19 inference(activate,[status(thm)],['0.7.1.0']),
% 0.81/1.19 [equation_1]).
% 0.81/1.19 cnf('0.8.0.0',axiom,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X1)) = bigC(X1,X2,X3) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.8.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X1)) = bigC(X1,X2,X3) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.81/1.19 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.81/1.19 cnf('0.8.2.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X1)) = bigC(X1,X2,X3) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_7]).
% 0.81/1.19 cnf('0.9.0.0',axiom,
% 0.81/1.19 ( product(product(a,c),product(c,b)) = product(a,b) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011')).
% 0.81/1.19 cnf('0.9.1.0',plain,
% 0.81/1.19 ( product(product(a,c),product(c,b)) = product(a,b) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.81/1.19 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.81/1.19 cnf('0.9.2.0',plain,
% 0.81/1.19 ( product(product(a,c),product(c,b)) = product(a,b) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_8]).
% 0.81/1.19 cnf('0.13.0.0',plain,
% 0.81/1.19 ( X1 = quotient(X2,difference(X1,X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.13.1.0',plain,
% 0.81/1.19 ( X1 = quotient(X2,difference(X1,X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.81/1.19 [weight('<41,5,1,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.13.2.0',plain,
% 0.81/1.19 ( quotient(X1,difference(X2,X1)) = X2 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_12]).
% 0.81/1.19 cnf('0.14.0.0',plain,
% 0.81/1.19 ( X1 = difference(quotient(X2,X1),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.14.1.0',plain,
% 0.81/1.19 ( X1 = difference(quotient(X2,X1),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.81/1.19 [weight('<41,6,4,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.14.2.0',plain,
% 0.81/1.19 ( difference(quotient(X1,X2),X1) = X2 ),
% 0.81/1.19 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_13]).
% 0.81/1.19 cnf('0.15.0.0',plain,
% 0.81/1.19 ( bigC(X1,X1,X2) = product(X1,product(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.8.2.0','0.2.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.15.1.0',plain,
% 0.81/1.19 ( bigC(X1,X1,X2) = product(X1,product(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.81/1.19 [weight('<59,8,2,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.15.2.0',plain,
% 0.81/1.19 ( product(X1,product(X2,X1)) = bigC(X1,X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_14]).
% 0.81/1.19 cnf('0.16.0.0',plain,
% 0.81/1.19 ( bigC(X1,X2,X1) = product(product(X1,X2),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.8.2.0','0.2.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.16.1.0',plain,
% 0.81/1.19 ( bigC(X1,X2,X1) = product(product(X1,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.81/1.19 [weight('<59,8,2,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.16.2.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X1) = bigC(X1,X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_15]).
% 0.81/1.19 cnf('0.17.0.0',plain,
% 0.81/1.19 ( bigC(X1,X1,quotient(X2,X1)) = product(X1,X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.15.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.17.1.0',plain,
% 0.81/1.19 ( bigC(X1,X1,quotient(X2,X1)) = product(X1,X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.81/1.19 [weight('<69,15,4,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.17.2.0',plain,
% 0.81/1.19 ( bigC(X1,X1,quotient(X2,X1)) = product(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_16]).
% 0.81/1.19 cnf('0.18.0.0',plain,
% 0.81/1.19 ( product(X1,X2) = difference(X2,bigC(X2,X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.15.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.18.1.0',plain,
% 0.81/1.19 ( product(X1,X2) = difference(X2,bigC(X2,X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.81/1.19 [weight('<69,15,6,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.18.2.0',plain,
% 0.81/1.19 ( difference(X1,bigC(X1,X1,X2)) = product(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_17]).
% 0.81/1.19 cnf('0.19.0.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X1) = product(X2,X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.16.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.19.1.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X1) = product(X2,X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.81/1.19 [weight('<69,16,1,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.19.2.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X1) = product(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_18]).
% 0.81/1.19 cnf('0.20.0.0',plain,
% 0.81/1.19 ( product(X1,X2) = quotient(bigC(X1,X2,X1),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.5.2.0','0.16.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.20.1.0',plain,
% 0.81/1.19 ( product(X1,X2) = quotient(bigC(X1,X2,X1),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.81/1.19 [weight('<69,16,5,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.20.2.0',plain,
% 0.81/1.19 ( quotient(bigC(X1,X2,X1),X1) = product(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_19]).
% 0.81/1.19 cnf('0.21.0.0',plain,
% 0.81/1.19 ( bigC(X1,X2,X3) = product(product(X1,X3),product(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.8.2.0','0.7.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.21.0.1',plain,
% 0.81/1.19 ( bigC(X1,X2,X3) = bigC(X1,X3,X2) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.21.0.0','0.8.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.21.1.0',plain,
% 0.81/1.19 ( bigC(X1,X2,X3) = bigC(X1,X3,X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.21.0.1']),
% 0.81/1.19 [weight('<80,8,7,[1,0,0,0]>')]).
% 0.81/1.19 cnf('0.21.2.0',plain,
% 0.81/1.19 ( bigC(X1,X2,X3) = bigC(X1,X3,X2) ),
% 0.81/1.19 inference(activate,[status(thm)],['0.21.1.0']),
% 0.81/1.19 [equation_2]).
% 0.81/1.19 cnf('0.22.0.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X1) = product(X2,X1) ),
% 0.81/1.19 inference(interreduction_right,[status(thm)],['0.19.2.0'])).
% 0.81/1.19 cnf('0.22.1.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X1) = product(X2,X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.81/1.19 [weight('<69,19,21,[0,0,0,0]>')]).
% 0.81/1.19 cnf('0.22.1.1',plain,
% 0.81/1.19 ( bigC(X1,X1,difference(X1,X2)) = product(X2,X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.22.1.0','0.21.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.22.2.0',plain,
% 0.81/1.19 ( bigC(X1,X1,difference(X1,X2)) = product(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.22.1.1',theory(equality)]),
% 0.81/1.19 [u,rule_20]).
% 0.81/1.19 cnf('0.23.0.0',plain,
% 0.81/1.19 ( product(difference(X1,X2),X1) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.18.2.0','0.22.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.23.1.0',plain,
% 0.81/1.19 ( product(difference(X1,X2),X1) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.81/1.19 [weight('<65,22,18,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.23.2.0',plain,
% 0.81/1.19 ( product(difference(X1,X2),X1) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_21]).
% 0.81/1.19 cnf('0.25.0.0',plain,
% 0.81/1.19 ( product(X1,X2) = quotient(bigC(X1,X1,X2),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.20.2.0','0.21.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.25.1.0',plain,
% 0.81/1.19 ( product(X1,X2) = quotient(bigC(X1,X1,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.81/1.19 [weight('<69,21,20,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.25.2.0',plain,
% 0.81/1.19 ( quotient(bigC(X1,X1,X2),X1) = product(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_23]).
% 0.81/1.19 cnf('0.26.0.0',plain,
% 0.81/1.19 ( product(X1,quotient(X2,X1)) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.25.2.0','0.17.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.26.1.0',plain,
% 0.81/1.19 ( product(X1,quotient(X2,X1)) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.81/1.19 [weight('<65,25,17,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.26.2.0',plain,
% 0.81/1.19 ( product(X1,quotient(X2,X1)) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_24]).
% 0.81/1.19 cnf('0.27.0.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X3) = product(X2,product(X3,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.8.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.27.1.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X3) = product(X2,product(X3,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.27.0.0']),
% 0.81/1.19 [weight('<83,8,1,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.27.2.0',plain,
% 0.81/1.19 ( bigC(X1,difference(X1,X2),X3) = product(X2,product(X3,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_25]).
% 0.81/1.19 cnf('0.28.0.0',plain,
% 0.81/1.19 ( bigC(X1,X2,quotient(X3,X1)) = product(product(X1,X2),X3) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.8.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.28.1.0',plain,
% 0.81/1.19 ( bigC(X1,X2,quotient(X3,X1)) = product(product(X1,X2),X3) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.81/1.19 [weight('<83,8,4,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.28.2.0',plain,
% 0.81/1.19 ( bigC(X1,X2,quotient(X3,X1)) = product(product(X1,X2),X3) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_26]).
% 0.81/1.19 cnf('0.29.0.0',plain,
% 0.81/1.19 ( product(X1,product(X2,X3)) = bigC(X3,X2,difference(X3,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.27.2.0','0.21.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.29.1.0',plain,
% 0.81/1.19 ( product(X1,product(X2,X3)) = bigC(X3,X2,difference(X3,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.81/1.19 [weight('<83,27,21,[1,0,0,0]>')]).
% 0.81/1.19 cnf('0.29.2.0',plain,
% 0.81/1.19 ( bigC(X1,X2,difference(X1,X3)) = product(X3,product(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_27]).
% 0.81/1.19 cnf('0.30.0.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X3) = bigC(X1,quotient(X3,X1),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.28.2.0','0.21.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.30.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X3) = bigC(X1,quotient(X3,X1),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.81/1.19 [weight('<83,28,21,[1,0,0,0]>')]).
% 0.81/1.19 cnf('0.30.2.0',plain,
% 0.81/1.19 ( bigC(X1,quotient(X2,X1),X3) = product(product(X1,X3),X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_28]).
% 0.81/1.19 cnf('0.35.0.0',plain,
% 0.81/1.19 ( quotient(X1,X2) = difference(X2,quotient(product(X2,X1),X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.35.1.0',plain,
% 0.81/1.19 ( quotient(X1,X2) = difference(X2,quotient(product(X2,X1),X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.81/1.19 [weight('<87,26,6,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.35.2.0',plain,
% 0.81/1.19 ( difference(X1,quotient(product(X1,X2),X1)) = quotient(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_33]).
% 0.81/1.19 cnf('0.44.0.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X2) = quotient(X2,product(X2,product(X2,X1))) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.44.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X2) = quotient(X2,product(X2,product(X2,X1))) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.44.0.0']),
% 0.81/1.19 [weight('<103,5,3,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.44.2.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,product(X1,X2))) = product(product(X2,X1),X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_42]).
% 0.81/1.19 cnf('0.45.0.0',plain,
% 0.81/1.19 ( product(X1,product(X1,X2)) = difference(product(product(X2,X1),X1),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.3.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.45.1.0',plain,
% 0.81/1.19 ( product(X1,product(X1,X2)) = difference(product(product(X2,X1),X1),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.45.0.0']),
% 0.81/1.19 [weight('<103,6,3,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.45.2.0',plain,
% 0.81/1.19 ( difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_43]).
% 0.81/1.19 cnf('0.46.0.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.46.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.46.0.0']),
% 0.81/1.19 [weight('<103,7,2,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.46.2.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_44]).
% 0.81/1.19 cnf('0.47.0.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.47.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.81/1.19 [weight('<103,7,2,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.47.2.0',plain,
% 0.81/1.19 ( product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_45]).
% 0.81/1.19 cnf('0.48.0.0',plain,
% 0.81/1.19 ( product(product(difference(X1,X2),X1),X1) = quotient(X1,product(X1,X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.44.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2.2','L')]).
% 0.81/1.19 cnf('0.48.0.1',plain,
% 0.81/1.19 ( product(difference(X1,product(X2,X1)),X1) = quotient(X1,product(X1,X2)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.48.0.0','0.23.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.48.0.2',plain,
% 0.81/1.19 ( difference(X1,product(product(X2,X1),X1)) = quotient(X1,product(X1,X2)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.48.0.1','0.23.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.48.1.0',plain,
% 0.81/1.19 ( difference(X1,product(product(X2,X1),X1)) = quotient(X1,product(X1,X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.48.0.2']),
% 0.81/1.19 [weight('<103,44,1,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.48.2.0',plain,
% 0.81/1.19 ( difference(X1,product(product(X2,X1),X1)) = quotient(X1,product(X1,X2)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_46]).
% 0.81/1.19 cnf('0.49.0.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,difference(X1,X2))) = difference(X1,product(difference(X1,product(X2,X1)),X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.48.2.0','0.23.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2.1','L')]).
% 0.81/1.19 cnf('0.49.0.1',plain,
% 0.81/1.19 ( quotient(X1,X2) = difference(X1,product(difference(X1,product(X2,X1)),X1)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.49.0.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.49.0.2',plain,
% 0.81/1.19 ( quotient(X1,X2) = difference(X1,difference(X1,product(product(X2,X1),X1))) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.49.0.1','0.23.2.0',theory(equality)]),
% 0.81/1.19 [pos('R.2','L')]).
% 0.81/1.19 cnf('0.49.0.3',plain,
% 0.81/1.19 ( quotient(X1,X2) = difference(X1,quotient(X1,product(X1,X2))) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.49.0.2','0.48.2.0',theory(equality)]),
% 0.81/1.19 [pos('R.2','L')]).
% 0.81/1.19 cnf('0.49.1.0',plain,
% 0.81/1.19 ( quotient(X1,X2) = difference(X1,quotient(X1,product(X1,X2))) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.49.0.3']),
% 0.81/1.19 [weight('<87,48,23,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.49.2.0',plain,
% 0.81/1.19 ( difference(X1,quotient(X1,product(X1,X2))) = quotient(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_47]).
% 0.81/1.19 cnf('0.50.0.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,X2)) = product(X1,quotient(X1,X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.1.2.0','0.49.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.50.1.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,X2)) = product(X1,quotient(X1,X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.50.0.0']),
% 0.81/1.19 [weight('<65,49,1,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.50.2.0',plain,
% 0.81/1.19 ( product(X1,quotient(X1,X2)) = quotient(X1,product(X1,X2)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_48]).
% 0.81/1.19 cnf('0.51.0.0',plain,
% 0.81/1.19 ( quotient(X1,difference(X1,X2)) = difference(X1,quotient(X1,X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.49.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2.2','L')]).
% 0.81/1.19 cnf('0.51.1.0',plain,
% 0.81/1.19 ( quotient(X1,difference(X1,X2)) = difference(X1,quotient(X1,X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.51.0.0']),
% 0.81/1.19 [weight('<65,49,1,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.51.2.0',plain,
% 0.81/1.19 ( quotient(X1,difference(X1,X2)) = difference(X1,quotient(X1,X2)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_49]).
% 0.81/1.19 cnf('0.52.0.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,difference(X2,X1))) = product(X1,X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.50.2.0','0.13.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.52.1.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,difference(X2,X1))) = product(X1,X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.52.0.0']),
% 0.81/1.19 [weight('<87,50,13,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.52.2.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,difference(X2,X1))) = product(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_50]).
% 0.81/1.19 cnf('0.53.0.0',plain,
% 0.81/1.19 ( product(X1,difference(X2,X1)) = difference(product(X1,X2),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.14.2.0','0.52.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.53.1.0',plain,
% 0.81/1.19 ( product(X1,difference(X2,X1)) = difference(product(X1,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.53.0.0']),
% 0.81/1.19 [weight('<65,52,14,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.53.2.0',plain,
% 0.81/1.19 ( product(X1,difference(X2,X1)) = difference(product(X1,X2),X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_51]).
% 0.81/1.19 cnf('0.54.0.0',plain,
% 0.81/1.19 ( difference(X1,X2) = difference(difference(X1,quotient(X1,X2)),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.14.2.0','0.51.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.54.1.0',plain,
% 0.81/1.19 ( difference(X1,X2) = difference(difference(X1,quotient(X1,X2)),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.54.0.0']),
% 0.81/1.19 [weight('<87,51,14,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.54.2.0',plain,
% 0.81/1.19 ( difference(difference(X1,quotient(X1,X2)),X1) = difference(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_52]).
% 0.81/1.19 cnf('0.55.0.0',plain,
% 0.81/1.19 ( difference(X1,difference(X2,X1)) = difference(difference(X1,X2),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.54.2.0','0.13.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.2','L')]).
% 0.81/1.19 cnf('0.55.1.0',plain,
% 0.81/1.19 ( difference(X1,difference(X2,X1)) = difference(difference(X1,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.55.0.0']),
% 0.81/1.19 [weight('<65,54,13,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.55.2.0',plain,
% 0.81/1.19 ( difference(difference(X1,X2),X1) = difference(X1,difference(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_53]).
% 0.81/1.19 cnf('0.56.0.0',plain,
% 0.81/1.19 ( difference(X1,X2) = difference(X2,difference(product(X2,X1),X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.53.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.56.1.0',plain,
% 0.81/1.19 ( difference(X1,X2) = difference(X2,difference(product(X2,X1),X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.81/1.19 [weight('<87,53,6,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.56.2.0',plain,
% 0.81/1.19 ( difference(X1,difference(product(X1,X2),X1)) = difference(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_54]).
% 0.81/1.19 cnf('0.57.0.0',plain,
% 0.81/1.19 ( product(X1,product(X1,quotient(X2,X1))) = difference(product(X2,X1),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.45.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.1','L')]).
% 0.81/1.19 cnf('0.57.0.1',plain,
% 0.81/1.19 ( product(X1,quotient(product(X1,X2),X1)) = difference(product(X2,X1),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.57.0.0','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.57.0.2',plain,
% 0.81/1.19 ( quotient(product(X1,product(X1,X2)),X1) = difference(product(X2,X1),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.57.0.1','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.57.1.0',plain,
% 0.81/1.19 ( quotient(product(X1,product(X1,X2)),X1) = difference(product(X2,X1),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.57.0.2']),
% 0.81/1.19 [weight('<103,45,4,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.57.2.0',plain,
% 0.81/1.19 ( quotient(product(X1,product(X1,X2)),X1) = difference(product(X2,X1),X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_55]).
% 0.81/1.19 cnf('0.58.0.0',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X2),X2) = quotient(product(X2,quotient(product(X2,X1),X2)),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.57.2.0','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.2','L')]).
% 0.81/1.19 cnf('0.58.0.1',plain,
% 0.81/1.19 ( difference(X1,X2) = quotient(product(X2,quotient(product(X2,X1),X2)),X2) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.58.0.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.58.0.2',plain,
% 0.81/1.19 ( difference(X1,X2) = quotient(quotient(product(X2,product(X2,X1)),X2),X2) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.58.0.1','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('R.1','L')]).
% 0.81/1.19 cnf('0.58.0.3',plain,
% 0.81/1.19 ( difference(X1,X2) = quotient(difference(product(X1,X2),X2),X2) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.58.0.2','0.57.2.0',theory(equality)]),
% 0.81/1.19 [pos('R.1','L')]).
% 0.81/1.19 cnf('0.58.1.0',plain,
% 0.81/1.19 ( difference(X1,X2) = quotient(difference(product(X1,X2),X2),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.58.0.3']),
% 0.81/1.19 [weight('<87,57,26,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.58.2.0',plain,
% 0.81/1.19 ( quotient(difference(product(X1,X2),X2),X2) = difference(X1,X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_56]).
% 0.81/1.19 cnf('0.59.0.0',plain,
% 0.81/1.19 ( difference(product(X1,X2),X2) = product(difference(X1,X2),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.4.2.0','0.58.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.59.1.0',plain,
% 0.81/1.19 ( difference(product(X1,X2),X2) = product(difference(X1,X2),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.59.0.0']),
% 0.81/1.19 [weight('<65,58,4,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.59.2.0',plain,
% 0.81/1.19 ( product(difference(X1,X2),X2) = difference(product(X1,X2),X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_57]).
% 0.81/1.19 cnf('0.60.0.0',plain,
% 0.81/1.19 ( difference(quotient(X1,X2),X2) = quotient(difference(X1,X2),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.58.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.1','L')]).
% 0.81/1.19 cnf('0.60.1.0',plain,
% 0.81/1.19 ( difference(quotient(X1,X2),X2) = quotient(difference(X1,X2),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.60.0.0']),
% 0.81/1.19 [weight('<65,58,4,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.60.2.0',plain,
% 0.81/1.19 ( quotient(difference(X1,X2),X2) = difference(quotient(X1,X2),X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_58]).
% 0.81/1.19 cnf('0.61.0.0',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X1),X1) = quotient(product(X1,quotient(X1,product(X1,X2))),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.57.2.0','0.50.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.2','L')]).
% 0.81/1.19 cnf('0.61.0.1',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X1),X1) = quotient(quotient(X1,product(X1,product(X1,X2))),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.61.0.0','0.50.2.0',theory(equality)]),
% 0.81/1.19 [pos('R.1','L')]).
% 0.81/1.19 cnf('0.61.0.2',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X1),X1) = quotient(product(product(X2,X1),X1),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.61.0.1','0.44.2.0',theory(equality)]),
% 0.81/1.19 [pos('R.1','L')]).
% 0.81/1.19 cnf('0.61.0.3',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X1),X1) = product(X2,X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.61.0.2','0.5.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.61.1.0',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X1),X1) = product(X2,X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.61.0.3']),
% 0.81/1.19 [weight('<87,57,50,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.61.2.0',plain,
% 0.81/1.19 ( difference(product(quotient(X1,X2),X1),X1) = product(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_59]).
% 0.81/1.19 cnf('0.62.0.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),X1) = quotient(X1,product(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.13.2.0','0.61.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.62.1.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),X1) = quotient(X1,product(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.62.0.0']),
% 0.81/1.19 [weight('<65,61,13,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.62.2.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),X1) = quotient(X1,product(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_60]).
% 0.81/1.19 cnf('0.63.0.0',plain,
% 0.81/1.19 ( difference(quotient(quotient(X1,X2),X1),X1) = quotient(X2,X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.60.2.0','0.14.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.63.1.0',plain,
% 0.81/1.19 ( difference(quotient(quotient(X1,X2),X1),X1) = quotient(X2,X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.63.0.0']),
% 0.81/1.19 [weight('<87,60,14,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.63.2.0',plain,
% 0.81/1.19 ( difference(quotient(quotient(X1,X2),X1),X1) = quotient(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_61]).
% 0.81/1.19 cnf('0.64.0.0',plain,
% 0.81/1.19 ( quotient(quotient(X1,X2),X1) = quotient(X1,quotient(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.13.2.0','0.63.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.64.1.0',plain,
% 0.81/1.19 ( quotient(quotient(X1,X2),X1) = quotient(X1,quotient(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.64.0.0']),
% 0.81/1.19 [weight('<65,63,13,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.64.2.0',plain,
% 0.81/1.19 ( quotient(quotient(X1,X2),X1) = quotient(X1,quotient(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_62]).
% 0.81/1.19 cnf('0.69.0.0',plain,
% 0.81/1.19 ( product(X1,product(difference(X1,X2),X3)) = product(X2,product(X1,X3)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.46.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.69.1.0',plain,
% 0.81/1.19 ( product(X1,product(difference(X1,X2),X3)) = product(X2,product(X1,X3)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.69.0.0']),
% 0.81/1.19 [weight('<103,46,1,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.69.2.0',plain,
% 0.81/1.19 ( product(X1,product(difference(X1,X2),X3)) = product(X2,product(X1,X3)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_67]).
% 0.81/1.19 cnf('0.70.0.0',plain,
% 0.81/1.19 ( product(X1,product(X2,X1)) = product(X2,difference(product(X2,X1),X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.69.2.0','0.59.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.70.0.1',plain,
% 0.81/1.19 ( bigC(X1,X1,X2) = product(X2,difference(product(X2,X1),X1)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.70.0.0','0.15.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.70.1.0',plain,
% 0.81/1.19 ( bigC(X1,X1,X2) = product(X2,difference(product(X2,X1),X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.70.0.1']),
% 0.81/1.19 [weight('<95,69,59,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.70.2.0',plain,
% 0.81/1.19 ( product(X1,difference(product(X1,X2),X2)) = bigC(X2,X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_68]).
% 0.81/1.19 cnf('0.73.0.0',plain,
% 0.81/1.19 ( bigC(X1,X1,quotient(X2,X1)) = product(quotient(X2,X1),difference(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.70.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2.1','L')]).
% 0.81/1.19 cnf('0.73.0.1',plain,
% 0.81/1.19 ( product(product(X1,X1),X2) = product(quotient(X2,X1),difference(X2,X1)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.73.0.0','0.28.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.73.0.2',plain,
% 0.81/1.19 ( product(X1,X2) = product(quotient(X2,X1),difference(X2,X1)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.73.0.1','0.2.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.73.1.0',plain,
% 0.81/1.19 ( product(X1,X2) = product(quotient(X2,X1),difference(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.73.0.2']),
% 0.81/1.19 [weight('<87,70,4,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.73.2.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),difference(X1,X2)) = product(X2,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_71]).
% 0.81/1.19 cnf('0.79.0.0',plain,
% 0.81/1.19 ( product(X1,product(X2,difference(X1,X3))) = product(product(X1,X2),X3) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.46.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.79.1.0',plain,
% 0.81/1.19 ( product(X1,product(X2,difference(X1,X3))) = product(product(X1,X2),X3) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.79.0.0']),
% 0.81/1.19 [weight('<103,46,1,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.79.2.0',plain,
% 0.81/1.19 ( product(X1,product(X2,difference(X1,X3))) = product(product(X1,X2),X3) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_77]).
% 0.81/1.19 cnf('0.80.0.0',plain,
% 0.81/1.19 ( product(product(quotient(X1,X2),X3),X2) = product(X1,product(X3,X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.47.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.80.1.0',plain,
% 0.81/1.19 ( product(product(quotient(X1,X2),X3),X2) = product(X1,product(X3,X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.80.0.0']),
% 0.81/1.19 [weight('<103,47,4,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.80.2.0',plain,
% 0.81/1.19 ( product(product(quotient(X1,X2),X3),X2) = product(X1,product(X3,X2)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.80.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_78]).
% 0.81/1.19 cnf('0.82.0.0',plain,
% 0.81/1.19 ( quotient(X1,product(X1,quotient(X2,X1))) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.48.2.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2.1','L')]).
% 0.81/1.19 cnf('0.82.0.1',plain,
% 0.81/1.19 ( quotient(X1,quotient(product(X1,X2),X1)) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.82.0.0','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.82.1.0',plain,
% 0.81/1.19 ( quotient(X1,quotient(product(X1,X2),X1)) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.82.0.1']),
% 0.81/1.19 [weight('<103,48,4,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.82.2.0',plain,
% 0.81/1.19 ( quotient(X1,quotient(product(X1,X2),X1)) = difference(X1,product(X2,X1)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.82.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_80]).
% 0.81/1.19 cnf('0.83.0.0',plain,
% 0.81/1.19 ( difference(product(difference(X1,X2),X1),X1) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.57.2.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.2','L')]).
% 0.81/1.19 cnf('0.83.0.1',plain,
% 0.81/1.19 ( difference(difference(X1,product(X2,X1)),X1) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.83.0.0','0.23.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.83.0.2',plain,
% 0.81/1.19 ( difference(X1,difference(product(X2,X1),X1)) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.83.0.1','0.55.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.83.1.0',plain,
% 0.81/1.19 ( difference(X1,difference(product(X2,X1),X1)) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.83.0.2']),
% 0.81/1.19 [weight('<103,57,1,[1,0,0,3]>')]).
% 0.81/1.19 cnf('0.83.2.0',plain,
% 0.81/1.19 ( difference(X1,difference(product(X2,X1),X1)) = quotient(product(X1,X2),X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.83.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_81]).
% 0.81/1.19 cnf('0.93.0.0',plain,
% 0.81/1.19 ( product(X1,difference(X2,X3)) = difference(X2,product(product(X2,X1),X3)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.79.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.93.1.0',plain,
% 0.81/1.19 ( product(X1,difference(X2,X3)) = difference(X2,product(product(X2,X1),X3)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.93.0.0']),
% 0.81/1.19 [weight('<103,79,6,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.93.2.0',plain,
% 0.81/1.19 ( difference(X1,product(product(X1,X2),X3)) = product(X2,difference(X1,X3)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.93.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_91]).
% 0.81/1.19 cnf('0.94.0.0',plain,
% 0.81/1.19 ( product(c,difference(a,product(c,b))) = difference(a,product(a,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.93.2.0','0.9.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.94.0.1',plain,
% 0.81/1.19 ( product(c,difference(a,product(c,b))) = b ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.94.0.0','0.6.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.94.1.0',plain,
% 0.81/1.19 ( product(c,difference(a,product(c,b))) = b ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.94.0.1']),
% 0.81/1.19 [weight('<71,93,9,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.94.2.0',plain,
% 0.81/1.19 ( product(c,difference(a,product(c,b))) = b ),
% 0.81/1.19 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_92]).
% 0.81/1.19 cnf('0.95.0.0',plain,
% 0.81/1.19 ( difference(a,product(c,b)) = difference(c,b) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.94.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.95.1.0',plain,
% 0.81/1.19 ( difference(a,product(c,b)) = difference(c,b) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.95.0.0']),
% 0.81/1.19 [weight('<53,94,6,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.95.2.0',plain,
% 0.81/1.19 ( difference(a,product(c,b)) = difference(c,b) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_93]).
% 0.81/1.19 cnf('0.96.0.0',plain,
% 0.81/1.19 ( product(c,b) = product(a,difference(c,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.1.2.0','0.95.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.96.1.0',plain,
% 0.81/1.19 ( product(c,b) = product(a,difference(c,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.96.0.0']),
% 0.81/1.19 [weight('<53,95,1,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.96.2.0',plain,
% 0.81/1.19 ( product(a,difference(c,b)) = product(c,b) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.96.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_94]).
% 0.81/1.19 cnf('0.97.0.0',plain,
% 0.81/1.19 ( product(product(c,a),b) = product(c,product(c,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.79.2.0','0.96.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.97.1.0',plain,
% 0.81/1.19 ( product(product(c,a),b) = product(c,product(c,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.97.0.0']),
% 0.81/1.19 [weight('<65,96,79,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.97.2.0',plain,
% 0.81/1.19 ( product(product(c,a),b) = product(c,product(c,b)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.97.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_95]).
% 0.81/1.19 cnf('0.100.0.0',plain,
% 0.81/1.19 ( product(c,a) = quotient(product(c,product(c,b)),b) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.5.2.0','0.97.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.100.1.0',plain,
% 0.81/1.19 ( product(c,a) = quotient(product(c,product(c,b)),b) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.100.0.0']),
% 0.81/1.19 [weight('<87,97,5,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.100.2.0',plain,
% 0.81/1.19 ( quotient(product(c,product(c,b)),b) = product(c,a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.100.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_98]).
% 0.81/1.19 cnf('0.101.0.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X2) = product(X1,difference(product(X2,X1),X2)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.79.2.0','0.53.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.101.1.0',plain,
% 0.81/1.19 ( product(product(X1,X2),X2) = product(X1,difference(product(X2,X1),X2)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.101.0.0']),
% 0.81/1.19 [weight('<103,79,53,[1,0,0,2]>')]).
% 0.81/1.19 cnf('0.101.2.0',plain,
% 0.81/1.19 ( product(X1,difference(product(X2,X1),X2)) = product(product(X1,X2),X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.101.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_99]).
% 0.81/1.19 cnf('0.102.0.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),X3) = quotient(product(X1,product(X3,X2)),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.5.2.0','0.80.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.102.1.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),X3) = quotient(product(X1,product(X3,X2)),X2) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.102.0.0']),
% 0.81/1.19 [weight('<103,80,5,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.102.2.0',plain,
% 0.81/1.19 ( quotient(product(X1,product(X2,X3)),X3) = product(quotient(X1,X3),X2) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_100]).
% 0.81/1.19 cnf('0.103.0.0',plain,
% 0.81/1.19 ( quotient(product(c,product(c,b)),b) = product(c,a) ),
% 0.81/1.19 inference(interreduction_right,[status(thm)],['0.100.2.0'])).
% 0.81/1.19 cnf('0.103.0.1',plain,
% 0.81/1.19 ( product(quotient(c,b),c) = product(c,a) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.103.0.0','0.102.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.103.0.2',plain,
% 0.81/1.19 ( quotient(c,product(b,c)) = product(c,a) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.103.0.1','0.62.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.103.1.0',plain,
% 0.81/1.19 ( quotient(c,product(b,c)) = product(c,a) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.103.0.2']),
% 0.81/1.19 [weight('<53,100,102,[0,0,0,0]>')]).
% 0.81/1.19 cnf('0.103.2.0',plain,
% 0.81/1.19 ( quotient(c,product(b,c)) = product(c,a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.103.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_101]).
% 0.81/1.19 cnf('0.105.0.0',plain,
% 0.81/1.19 ( product(b,c) = difference(product(c,a),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.14.2.0','0.103.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.105.1.0',plain,
% 0.81/1.19 ( product(b,c) = difference(product(c,a),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.105.0.0']),
% 0.81/1.19 [weight('<53,103,14,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.105.2.0',plain,
% 0.81/1.19 ( difference(product(c,a),c) = product(b,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.105.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_103]).
% 0.81/1.19 cnf('0.106.0.0',plain,
% 0.81/1.19 ( quotient(c,quotient(product(b,c),c)) = quotient(product(c,a),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.64.2.0','0.103.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.106.0.1',plain,
% 0.81/1.19 ( quotient(c,b) = quotient(product(c,a),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.106.0.0','0.5.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.106.1.0',plain,
% 0.81/1.19 ( quotient(c,b) = quotient(product(c,a),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.106.0.1']),
% 0.81/1.19 [weight('<53,103,64,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.106.2.0',plain,
% 0.81/1.19 ( quotient(product(c,a),c) = quotient(c,b) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_104]).
% 0.81/1.19 cnf('0.108.0.0',plain,
% 0.81/1.19 ( difference(a,c) = difference(c,product(b,c)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.56.2.0','0.105.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.108.1.0',plain,
% 0.81/1.19 ( difference(a,c) = difference(c,product(b,c)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.108.0.0']),
% 0.81/1.19 [weight('<53,105,56,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.108.2.0',plain,
% 0.81/1.19 ( difference(c,product(b,c)) = difference(a,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_106]).
% 0.81/1.19 cnf('0.109.0.0',plain,
% 0.81/1.19 ( quotient(a,c) = difference(c,quotient(c,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.35.2.0','0.106.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.109.1.0',plain,
% 0.81/1.19 ( quotient(a,c) = difference(c,quotient(c,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.109.0.0']),
% 0.81/1.19 [weight('<53,106,35,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.109.2.0',plain,
% 0.81/1.19 ( difference(c,quotient(c,b)) = quotient(a,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_107]).
% 0.81/1.19 cnf('0.111.0.0',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(a,product(b,c)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.101.2.0','0.105.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.111.1.0',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(a,product(b,c)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.111.0.0']),
% 0.81/1.19 [weight('<65,105,101,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.111.2.0',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(a,product(b,c)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.111.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_109]).
% 0.81/1.19 cnf('0.115.0.0',plain,
% 0.81/1.19 ( difference(c,product(a,c)) = quotient(c,quotient(c,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.82.2.0','0.106.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.115.1.0',plain,
% 0.81/1.19 ( difference(c,product(a,c)) = quotient(c,quotient(c,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.115.0.0']),
% 0.81/1.19 [weight('<65,106,82,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.115.2.0',plain,
% 0.81/1.19 ( quotient(c,quotient(c,b)) = difference(c,product(a,c)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.115.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_113]).
% 0.81/1.19 cnf('0.116.0.0',plain,
% 0.81/1.19 ( difference(c,difference(product(b,c),c)) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.55.2.0','0.108.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.116.0.1',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.116.0.0','0.83.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.116.1.0',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.116.0.1']),
% 0.81/1.19 [weight('<65,108,55,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.116.2.0',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.116.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_114]).
% 0.81/1.19 cnf('0.139.0.0',plain,
% 0.81/1.19 ( product(product(c,a),product(X1,c)) = product(product(quotient(c,b),X1),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.80.2.0','0.106.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1.1','L')]).
% 0.81/1.19 cnf('0.139.0.1',plain,
% 0.81/1.19 ( bigC(c,a,X1) = product(product(quotient(c,b),X1),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.139.0.0','0.8.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.139.1.0',plain,
% 0.81/1.19 ( bigC(c,a,X1) = product(product(quotient(c,b),X1),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.139.0.1']),
% 0.81/1.19 [weight('<95,106,80,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.139.2.0',plain,
% 0.81/1.19 ( product(product(quotient(c,b),X1),c) = bigC(c,a,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_137]).
% 0.81/1.19 cnf('0.140.0.0',plain,
% 0.81/1.19 ( bigC(c,a,difference(c,b)) = product(product(b,c),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.139.2.0','0.73.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.140.0.1',plain,
% 0.81/1.19 ( product(b,product(a,c)) = product(product(b,c),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.140.0.0','0.29.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.140.1.0',plain,
% 0.81/1.19 ( product(b,product(a,c)) = product(product(b,c),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.140.0.1']),
% 0.81/1.19 [weight('<65,139,73,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.140.2.0',plain,
% 0.81/1.19 ( product(product(b,c),c) = product(b,product(a,c)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.140.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_138]).
% 0.81/1.19 cnf('0.142.0.0',plain,
% 0.81/1.19 ( product(c,difference(b,c)) = difference(b,product(b,product(a,c))) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.93.2.0','0.140.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.142.0.1',plain,
% 0.81/1.19 ( difference(product(c,b),c) = difference(b,product(b,product(a,c))) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.142.0.0','0.53.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.142.0.2',plain,
% 0.81/1.19 ( difference(product(c,b),c) = product(a,c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.142.0.1','0.6.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.142.1.0',plain,
% 0.81/1.19 ( difference(product(c,b),c) = product(a,c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.142.0.2']),
% 0.81/1.19 [weight('<53,140,93,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.142.2.0',plain,
% 0.81/1.19 ( difference(product(c,b),c) = product(a,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_140]).
% 0.81/1.19 cnf('0.144.0.0',plain,
% 0.81/1.19 ( product(c,b) = quotient(c,product(a,c)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.13.2.0','0.142.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.144.1.0',plain,
% 0.81/1.19 ( product(c,b) = quotient(c,product(a,c)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.144.0.0']),
% 0.81/1.19 [weight('<53,142,13,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.144.2.0',plain,
% 0.81/1.19 ( quotient(c,product(a,c)) = product(c,b) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.144.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_142]).
% 0.81/1.19 cnf('0.145.0.0',plain,
% 0.81/1.19 ( difference(b,c) = difference(c,product(a,c)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.56.2.0','0.142.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.145.1.0',plain,
% 0.81/1.19 ( difference(b,c) = difference(c,product(a,c)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.145.0.0']),
% 0.81/1.19 [weight('<53,142,56,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.145.2.0',plain,
% 0.81/1.19 ( difference(c,product(a,c)) = difference(b,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.145.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_143]).
% 0.81/1.19 cnf('0.146.0.0',plain,
% 0.81/1.19 ( quotient(c,quotient(c,b)) = difference(c,product(a,c)) ),
% 0.81/1.19 inference(interreduction_right,[status(thm)],['0.115.2.0'])).
% 0.81/1.19 cnf('0.146.0.1',plain,
% 0.81/1.19 ( quotient(c,quotient(c,b)) = difference(b,c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.146.0.0','0.145.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.146.1.0',plain,
% 0.81/1.19 ( quotient(c,quotient(c,b)) = difference(b,c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.146.0.1']),
% 0.81/1.19 [weight('<53,115,145,[0,0,0,0]>')]).
% 0.81/1.19 cnf('0.146.2.0',plain,
% 0.81/1.19 ( quotient(c,quotient(c,b)) = difference(b,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.146.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_144]).
% 0.81/1.19 cnf('0.147.0.0',plain,
% 0.81/1.19 ( quotient(c,quotient(product(a,c),c)) = quotient(product(c,b),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.64.2.0','0.144.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.147.0.1',plain,
% 0.81/1.19 ( quotient(c,a) = quotient(product(c,b),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.147.0.0','0.5.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.147.0.2',plain,
% 0.81/1.19 ( quotient(c,a) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.147.0.1','0.116.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.147.1.0',plain,
% 0.81/1.19 ( quotient(c,a) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.147.0.2']),
% 0.81/1.19 [weight('<53,144,64,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.147.2.0',plain,
% 0.81/1.19 ( difference(difference(a,c),c) = quotient(c,a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.147.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_145]).
% 0.81/1.19 cnf('0.148.0.0',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = difference(difference(a,c),c) ),
% 0.81/1.19 inference(interreduction_right,[status(thm)],['0.116.2.0'])).
% 0.81/1.19 cnf('0.148.0.1',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = quotient(c,a) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.148.0.0','0.147.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.148.1.0',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = quotient(c,a) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.148.0.1']),
% 0.81/1.19 [weight('<53,116,147,[0,0,0,0]>')]).
% 0.81/1.19 cnf('0.148.2.0',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = quotient(c,a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.148.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_146]).
% 0.81/1.19 cnf('0.153.0.0',plain,
% 0.81/1.19 ( difference(c,product(product(a,c),c)) = product(difference(b,c),c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.23.2.0','0.145.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.153.0.1',plain,
% 0.81/1.19 ( quotient(c,product(c,a)) = product(difference(b,c),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.153.0.0','0.48.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.153.0.2',plain,
% 0.81/1.19 ( quotient(c,product(c,a)) = difference(product(b,c),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.153.0.1','0.59.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.153.1.0',plain,
% 0.81/1.19 ( quotient(c,product(c,a)) = difference(product(b,c),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.153.0.2']),
% 0.81/1.19 [weight('<65,145,23,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.153.2.0',plain,
% 0.81/1.19 ( quotient(c,product(c,a)) = difference(product(b,c),c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_151]).
% 0.81/1.19 cnf('0.157.0.0',plain,
% 0.81/1.19 ( c = product(difference(b,c),quotient(c,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.4.2.0','0.146.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.157.1.0',plain,
% 0.81/1.19 ( c = product(difference(b,c),quotient(c,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.157.0.0']),
% 0.81/1.19 [weight('<71,146,4,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.157.2.0',plain,
% 0.81/1.19 ( product(difference(b,c),quotient(c,b)) = c ),
% 0.81/1.19 inference(orient,[status(thm)],['0.157.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_155]).
% 0.81/1.19 cnf('0.172.0.0',plain,
% 0.81/1.19 ( product(product(c,X1),product(c,b)) = bigC(c,quotient(c,a),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.30.2.0','0.148.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.172.0.1',plain,
% 0.81/1.19 ( product(c,product(X1,b)) = bigC(c,quotient(c,a),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.172.0.0','0.46.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.172.1.0',plain,
% 0.81/1.19 ( product(c,product(X1,b)) = bigC(c,quotient(c,a),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.172.0.1']),
% 0.81/1.19 [weight('<83,148,30,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.172.2.0',plain,
% 0.81/1.19 ( bigC(c,quotient(c,a),X1) = product(c,product(X1,b)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.172.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_170]).
% 0.81/1.19 cnf('0.182.0.0',plain,
% 0.81/1.19 ( product(c,product(b,quotient(c,b))) = product(b,c) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.69.2.0','0.157.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.182.0.1',plain,
% 0.81/1.19 ( product(c,quotient(product(b,c),b)) = product(b,c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.182.0.0','0.26.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.182.1.0',plain,
% 0.81/1.19 ( product(c,quotient(product(b,c),b)) = product(b,c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.182.0.1']),
% 0.81/1.19 [weight('<87,157,69,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.182.2.0',plain,
% 0.81/1.19 ( product(c,quotient(product(b,c),b)) = product(b,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.182.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_180]).
% 0.81/1.19 cnf('0.184.0.0',plain,
% 0.81/1.19 ( quotient(product(b,c),b) = difference(c,product(b,c)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.6.2.0','0.182.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.184.0.1',plain,
% 0.81/1.19 ( quotient(product(b,c),b) = difference(a,c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.184.0.0','0.108.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.184.1.0',plain,
% 0.81/1.19 ( quotient(product(b,c),b) = difference(a,c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.184.0.1']),
% 0.81/1.19 [weight('<53,182,6,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.184.2.0',plain,
% 0.81/1.19 ( quotient(product(b,c),b) = difference(a,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.184.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_182]).
% 0.81/1.19 cnf('0.185.0.0',plain,
% 0.81/1.19 ( product(b,c) = product(difference(a,c),b) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.4.2.0','0.184.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.185.1.0',plain,
% 0.81/1.19 ( product(b,c) = product(difference(a,c),b) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.185.0.0']),
% 0.81/1.19 [weight('<53,184,4,[0,0,0,1]>')]).
% 0.81/1.19 cnf('0.185.2.0',plain,
% 0.81/1.19 ( product(difference(a,c),b) = product(b,c) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.185.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_183]).
% 0.81/1.19 cnf('0.193.0.0',plain,
% 0.81/1.19 ( product(c,product(a,b)) = product(a,product(b,c)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.69.2.0','0.185.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.193.1.0',plain,
% 0.81/1.19 ( product(c,product(a,b)) = product(a,product(b,c)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.193.0.0']),
% 0.81/1.19 [weight('<65,185,69,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.193.2.0',plain,
% 0.81/1.19 ( product(a,product(b,c)) = product(c,product(a,b)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.193.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_191]).
% 0.81/1.19 cnf('0.194.0.0',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(a,product(b,c)) ),
% 0.81/1.19 inference(interreduction_right,[status(thm)],['0.111.2.0'])).
% 0.81/1.19 cnf('0.194.0.1',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(c,product(a,b)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.194.0.0','0.193.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.194.1.0',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(c,product(a,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.194.0.1']),
% 0.81/1.19 [weight('<65,111,193,[0,0,0,0]>')]).
% 0.81/1.19 cnf('0.194.2.0',plain,
% 0.81/1.19 ( product(product(a,c),c) = product(c,product(a,b)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.194.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_192]).
% 0.81/1.19 cnf('0.195.0.0',plain,
% 0.81/1.19 ( quotient(c,product(c,a)) = difference(c,product(c,product(a,b))) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.48.2.0','0.194.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.195.0.1',plain,
% 0.81/1.19 ( difference(product(b,c),c) = difference(c,product(c,product(a,b))) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.195.0.0','0.153.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.195.0.2',plain,
% 0.81/1.19 ( difference(product(b,c),c) = product(a,b) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.195.0.1','0.6.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.195.1.0',plain,
% 0.81/1.19 ( difference(product(b,c),c) = product(a,b) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.195.0.2']),
% 0.81/1.19 [weight('<53,194,48,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.195.2.0',plain,
% 0.81/1.19 ( difference(product(b,c),c) = product(a,b) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.195.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_193]).
% 0.81/1.19 cnf('0.204.0.0',plain,
% 0.81/1.19 ( quotient(product(c,b),c) = difference(c,product(a,b)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.83.2.0','0.195.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.204.0.1',plain,
% 0.81/1.19 ( quotient(c,a) = difference(c,product(a,b)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.204.0.0','0.148.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.204.1.0',plain,
% 0.81/1.19 ( quotient(c,a) = difference(c,product(a,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.204.0.1']),
% 0.81/1.19 [weight('<53,195,83,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.204.2.0',plain,
% 0.81/1.19 ( difference(c,product(a,b)) = quotient(c,a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.204.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_202]).
% 0.81/1.19 cnf('0.430.0.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),difference(X1,X3)) = quotient(product(X3,product(X1,X2)),X2) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.102.2.0','0.69.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.430.0.1',plain,
% 0.81/1.19 ( product(quotient(X1,X2),difference(X1,X3)) = product(quotient(X3,X2),X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.430.0.0','0.102.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.430.1.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),difference(X1,X3)) = product(quotient(X3,X2),X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.430.0.1']),
% 0.81/1.19 [weight('<103,102,69,[1,0,0,1]>')]).
% 0.81/1.19 cnf('0.430.2.0',plain,
% 0.81/1.19 ( product(quotient(X1,X2),difference(X1,X3)) = product(quotient(X3,X2),X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.430.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_428]).
% 0.81/1.19 cnf('0.432.0.0',plain,
% 0.81/1.19 ( product(quotient(c,b),product(X1,c)) = bigC(c,quotient(a,c),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.27.2.0','0.109.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.432.0.1',plain,
% 0.81/1.19 ( product(quotient(c,b),product(X1,c)) = product(product(c,X1),a) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.432.0.0','0.30.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.432.1.0',plain,
% 0.81/1.19 ( product(quotient(c,b),product(X1,c)) = product(product(c,X1),a) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.432.0.1']),
% 0.81/1.19 [weight('<103,109,27,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.432.2.0',plain,
% 0.81/1.19 ( product(quotient(c,b),product(X1,c)) = product(product(c,X1),a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.432.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_430]).
% 0.81/1.19 cnf('0.433.0.0',plain,
% 0.81/1.19 ( product(product(c,difference(c,X1)),a) = product(quotient(c,b),difference(c,product(X1,c))) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.432.2.0','0.23.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.433.0.1',plain,
% 0.81/1.19 ( product(X1,a) = product(quotient(c,b),difference(c,product(X1,c))) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.433.0.0','0.1.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.1','L')]).
% 0.81/1.19 cnf('0.433.0.2',plain,
% 0.81/1.19 ( product(X1,a) = product(quotient(product(X1,c),b),c) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.433.0.1','0.430.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.433.1.0',plain,
% 0.81/1.19 ( product(X1,a) = product(quotient(product(X1,c),b),c) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.433.0.2']),
% 0.81/1.19 [weight('<87,432,23,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.433.2.0',plain,
% 0.81/1.19 ( product(quotient(product(X1,c),b),c) = product(X1,a) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.433.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_431]).
% 0.81/1.19 cnf('0.483.0.0',plain,
% 0.81/1.19 ( product(product(a,b),product(X1,c)) = bigC(c,quotient(c,a),X1) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.27.2.0','0.204.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.483.0.1',plain,
% 0.81/1.19 ( product(product(a,b),product(X1,c)) = product(c,product(X1,b)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.483.0.0','0.172.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.483.1.0',plain,
% 0.81/1.19 ( product(product(a,b),product(X1,c)) = product(c,product(X1,b)) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.483.0.1']),
% 0.81/1.19 [weight('<103,204,27,[0,0,0,2]>')]).
% 0.81/1.19 cnf('0.483.2.0',plain,
% 0.81/1.19 ( product(product(a,b),product(X1,c)) = product(c,product(X1,b)) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.483.1.0',theory(equality)]),
% 0.81/1.19 [u,rule_481]).
% 0.81/1.19 cnf('0.484.0.0',plain,
% 0.81/1.19 ( product(c,product(quotient(product(X1,c),b),b)) = product(product(a,b),product(X1,a)) ),
% 0.81/1.19 inference(cp,[status(thm)],['0.483.2.0','0.433.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.484.0.1',plain,
% 0.81/1.19 ( product(c,product(X1,c)) = product(product(a,b),product(X1,a)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.484.0.0','0.4.2.0',theory(equality)]),
% 0.81/1.19 [pos('L.2','L')]).
% 0.81/1.19 cnf('0.484.0.2',plain,
% 0.81/1.19 ( bigC(c,c,X1) = product(product(a,b),product(X1,a)) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.484.0.1','0.15.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('0.484.0.3',plain,
% 0.81/1.19 ( bigC(c,c,X1) = bigC(a,b,X1) ),
% 0.81/1.19 inference(reduction,[status(thm)],['0.484.0.2','0.8.2.0',theory(equality)]),
% 0.81/1.19 [pos('R','L')]).
% 0.81/1.19 cnf('0.484.1.0',plain,
% 0.81/1.19 ( bigC(c,c,X1) = bigC(a,b,X1) ),
% 0.81/1.19 inference(weigh,[status(thm)],['0.484.0.3']),
% 0.81/1.19 [weight('<44,483,433,[1,0,0,4]>')]).
% 0.81/1.19 cnf('0.484.2.0',plain,
% 0.81/1.19 ( bigC(a,b,X1) = bigC(c,c,X1) ),
% 0.81/1.19 inference(orient,[status(thm)],['0.484.1.0',theory(equality)]),
% 0.81/1.19 [x,rule_482]).
% 0.81/1.19 cnf('1.0.0.0',conjecture,
% 0.81/1.19 ( bigC(a,b,x0) = bigC(c,c,x0) ),
% 0.81/1.19 file('/tmp/WALDMEISTER_32323_n011',conjecture_1)).
% 0.81/1.19 cnf('1.0.0.1',plain,
% 0.81/1.19 ( bigC(c,c,x0) = bigC(c,c,x0) ),
% 0.81/1.19 inference(reduction,[status(thm)],['1.0.0.0','0.484.2.0',theory(equality)]),
% 0.81/1.19 [pos('L','L')]).
% 0.81/1.19 cnf('1.0.0.2',plain,
% 0.81/1.19 ( $true ),
% 0.81/1.19 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.81/1.19 [conjecture_1]).
% 0.81/1.19
% 0.81/1.19 Proved Goals:
% 0.81/1.19 No. 1: bigC(a,b,x0) ?= bigC(c,c,x0) joined, current: bigC(c,c,x0) = bigC(c,c,x0)
% 0.81/1.19 1 goal was specified, which was proved.
% 0.81/1.19 % SZS output end CNFRefutation
% 0.81/1.19 #END OF PROOF
% 0.81/1.19
% 0.81/1.19 Problem WALDMEISTER_32323_n011
% 0.81/1.19 CPs.gen 16495
% 0.81/1.19 CPs.reexp 0
% 0.81/1.19 Select 881
% 0.81/1.19 R 482
% 0.81/1.19 E 2
% 0.81/1.19 vsize 7.0M
% 0.81/1.19 rss 4.3M
% 0.81/1.19 process.time 0.130s
% 0.81/1.19 wallclock.time 0.130s
% 0.81/1.19 status S
% 0.81/1.19
% 0.81/1.19
% 0.81/1.19 Waldmeister states: Goal proved.
% 0.81/1.19 % SZS status Unsatisfiable
%------------------------------------------------------------------------------