TSTP Solution File: GRP772-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP772-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:28:29 EDT 2022
% Result : Unsatisfiable 3.58s 3.99s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP772-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n005.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 06:56:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.60/1.00 ********************************************************************************
% 0.60/1.00 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/1.00 * |/ | \/ | *
% 0.60/1.00 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/1.00 * A. Jaeger and B. Loechner | | *
% 0.60/1.00 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/1.00 ********************************************************************************
% 0.60/1.00
% 0.60/1.00
% 0.60/1.00 Goals:
% 0.60/1.00 ------
% 0.60/1.00
% 0.60/1.00 ( 1) a(x0,x1,x1) ?=? a(x1,x1,x0)
% 0.60/1.00
% 0.60/1.00 Detected structure: Loop
% 0.60/1.00 ********************************************************************************
% 0.60/1.00 ****************************** COMPLETION - PROOF ******************************
% 0.60/1.00 ********************************************************************************
% 0.60/1.00
% 3.58/3.99 joined goal: 1 a(x0,x1,x1) ?= a(x1,x1,x0) to a(x1,x1,x0)
% 3.58/3.99 goal joined
% 3.58/3.99 % SZS status Unsatisfiable
% 3.58/3.99 #START OF PROOF
% 3.58/3.99 % SZS output start CNFRefutation
% 3.58/3.99 cnf('0.1.0.0',axiom,
% 3.58/3.99 ( X1 = product(X2,difference(X2,X1)) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.1.1.0',plain,
% 3.58/3.99 ( X1 = product(X2,difference(X2,X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.1.0.0']),
% 3.58/3.99 [weight('<0,0,0,[0,0,0,1]>')]).
% 3.58/3.99 cnf('0.1.2.0',plain,
% 3.58/3.99 ( product(X1,difference(X1,X2)) = X2 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_1]).
% 3.58/3.99 cnf('0.2.0.0',axiom,
% 3.58/3.99 ( X1 = product(X1,one) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.2.1.0',plain,
% 3.58/3.99 ( X1 = product(X1,one) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2.0.0']),
% 3.58/3.99 [weight('<1,0,0,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.2.2.0',plain,
% 3.58/3.99 ( product(X1,one) = X1 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_2]).
% 3.58/3.99 cnf('0.3.0.0',axiom,
% 3.58/3.99 ( X1 = product(quotient(X1,X2),X2) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.3.1.0',plain,
% 3.58/3.99 ( X1 = product(quotient(X1,X2),X2) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.3.0.0']),
% 3.58/3.99 [weight('<2,0,0,[0,0,0,3]>')]).
% 3.58/3.99 cnf('0.3.2.0',plain,
% 3.58/3.99 ( product(quotient(X1,X2),X2) = X1 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_3]).
% 3.58/3.99 cnf('0.4.0.0',axiom,
% 3.58/3.99 ( X1 = product(one,X1) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.4.1.0',plain,
% 3.58/3.99 ( X1 = product(one,X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.4.0.0']),
% 3.58/3.99 [weight('<3,0,0,[0,0,0,4]>')]).
% 3.58/3.99 cnf('0.4.2.0',plain,
% 3.58/3.99 ( product(one,X1) = X1 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_4]).
% 3.58/3.99 cnf('0.5.0.0',axiom,
% 3.58/3.99 ( X1 = quotient(product(X1,X2),X2) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.5.1.0',plain,
% 3.58/3.99 ( X1 = quotient(product(X1,X2),X2) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.5.0.0']),
% 3.58/3.99 [weight('<4,0,0,[0,0,0,5]>')]).
% 3.58/3.99 cnf('0.5.2.0',plain,
% 3.58/3.99 ( quotient(product(X1,X2),X2) = X1 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_5]).
% 3.58/3.99 cnf('0.6.0.0',axiom,
% 3.58/3.99 ( X1 = difference(X2,product(X2,X1)) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.6.1.0',plain,
% 3.58/3.99 ( X1 = difference(X2,product(X2,X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.6.0.0']),
% 3.58/3.99 [weight('<5,0,0,[0,0,0,6]>')]).
% 3.58/3.99 cnf('0.6.2.0',plain,
% 3.58/3.99 ( difference(X1,product(X1,X2)) = X2 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_6]).
% 3.58/3.99 cnf('0.11.0.0',axiom,
% 3.58/3.99 ( product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.11.1.0',plain,
% 3.58/3.99 ( product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.11.0.0']),
% 3.58/3.99 [weight('<10,0,0,[0,0,0,11]>')]).
% 3.58/3.99 cnf('0.11.2.0',plain,
% 3.58/3.99 ( product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_11]).
% 3.58/3.99 cnf('0.12.0.0',axiom,
% 3.58/3.99 ( product(X1,j(X1)) = product(i(X1),X1) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.12.1.0',plain,
% 3.58/3.99 ( product(X1,j(X1)) = product(i(X1),X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.12.0.0']),
% 3.58/3.99 [weight('<11,0,0,[0,0,0,12]>')]).
% 3.58/3.99 cnf('0.12.2.0',plain,
% 3.58/3.99 ( product(i(X1),X1) = product(X1,j(X1)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_12]).
% 3.58/3.99 cnf('0.15.0.0',axiom,
% 3.58/3.99 ( product(product(a(X1,X2,X3),X4),X5) = product(a(X1,X2,X3),product(X4,X5)) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.15.1.0',plain,
% 3.58/3.99 ( product(product(a(X1,X2,X3),X4),X5) = product(a(X1,X2,X3),product(X4,X5)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.15.0.0']),
% 3.58/3.99 [weight('<14,0,0,[0,0,0,15]>')]).
% 3.58/3.99 cnf('0.15.2.0',plain,
% 3.58/3.99 ( product(product(a(X1,X2,X3),X4),X5) = product(a(X1,X2,X3),product(X4,X5)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_15]).
% 3.58/3.99 cnf('0.20.0.0',axiom,
% 3.58/3.99 ( product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.20.1.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.20.0.0']),
% 3.58/3.99 [weight('<19,0,0,[0,0,0,20]>')]).
% 3.58/3.99 cnf('0.20.2.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one ),
% 3.58/3.99 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_20]).
% 3.58/3.99 cnf('0.21.0.0',axiom,
% 3.58/3.99 ( product(i(X1),X1) = eta(X1) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.21.1.0',plain,
% 3.58/3.99 ( product(i(X1),X1) = eta(X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.21.0.0']),
% 3.58/3.99 [weight('<20,0,0,[0,0,0,21]>')]).
% 3.58/3.99 cnf('0.21.1.1',plain,
% 3.58/3.99 ( product(X1,j(X1)) = eta(X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.21.1.0','0.12.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.21.2.0',plain,
% 3.58/3.99 ( product(X1,j(X1)) = eta(X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.21.1.1',theory(equality)]),
% 3.58/3.99 [u,rule_21]).
% 3.58/3.99 cnf('0.25.0.0',axiom,
% 3.58/3.99 ( j(X1) = quotient(one,X1) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.25.1.0',plain,
% 3.58/3.99 ( j(X1) = quotient(one,X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.25.0.0']),
% 3.58/3.99 [weight('<24,0,0,[0,0,0,25]>')]).
% 3.58/3.99 cnf('0.25.2.0',plain,
% 3.58/3.99 ( quotient(one,X1) = j(X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_25]).
% 3.58/3.99 cnf('0.26.0.0',axiom,
% 3.58/3.99 ( a(X1,X2,X3) = a(j(X3),X1,X2) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.26.1.0',plain,
% 3.58/3.99 ( a(X1,X2,X3) = a(j(X3),X1,X2) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.26.0.0']),
% 3.58/3.99 [weight('<25,0,0,[0,0,0,26]>')]).
% 3.58/3.99 cnf('0.26.2.0',plain,
% 3.58/3.99 ( a(j(X1),X2,X3) = a(X2,X3,X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_26]).
% 3.58/3.99 cnf('0.27.0.0',axiom,
% 3.58/3.99 ( a(X1,j(X2),X3) = a(X1,i(X2),X3) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.27.1.0',plain,
% 3.58/3.99 ( a(X1,j(X2),X3) = a(X1,i(X2),X3) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.27.0.0']),
% 3.58/3.99 [weight('<26,0,0,[0,0,0,27]>')]).
% 3.58/3.99 cnf('0.27.2.0',plain,
% 3.58/3.99 ( a(X1,j(X2),X3) = a(X1,i(X2),X3) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_27]).
% 3.58/3.99 cnf('0.28.0.0',axiom,
% 3.58/3.99 ( a(j(X1),X2,X3) = a(i(X1),X2,X3) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.28.1.0',plain,
% 3.58/3.99 ( a(j(X1),X2,X3) = a(i(X1),X2,X3) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.28.0.0']),
% 3.58/3.99 [weight('<27,0,0,[0,0,0,28]>')]).
% 3.58/3.99 cnf('0.28.1.1',plain,
% 3.58/3.99 ( a(X2,X3,X1) = a(i(X1),X2,X3) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.28.1.0','0.26.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.28.2.0',plain,
% 3.58/3.99 ( a(i(X1),X2,X3) = a(X2,X3,X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.28.1.1',theory(equality)]),
% 3.58/3.99 [x,rule_28]).
% 3.58/3.99 cnf('0.29.0.0',axiom,
% 3.58/3.99 ( i(X1) = difference(X1,one) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.29.1.0',plain,
% 3.58/3.99 ( i(X1) = difference(X1,one) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.29.0.0']),
% 3.58/3.99 [weight('<28,0,0,[0,0,0,29]>')]).
% 3.58/3.99 cnf('0.29.2.0',plain,
% 3.58/3.99 ( difference(X1,one) = i(X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_29]).
% 3.58/3.99 cnf('0.31.0.0',axiom,
% 3.58/3.99 ( quotient(product(X1,product(X2,X3)),X3) = difference(X3,product(product(X3,X1),X2)) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.31.1.0',plain,
% 3.58/3.99 ( quotient(product(X1,product(X2,X3)),X3) = difference(X3,product(product(X3,X1),X2)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.31.0.0']),
% 3.58/3.99 [weight('<30,0,0,[0,0,0,31]>')]).
% 3.58/3.99 cnf('0.31.2.0',plain,
% 3.58/3.99 ( quotient(product(X1,product(X2,X3)),X3) = difference(X3,product(product(X3,X1),X2)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_31]).
% 3.58/3.99 cnf('0.32.0.0',axiom,
% 3.58/3.99 ( quotient(quotient(product(X1,product(X2,X3)),X3),X2) = difference(product(X2,X3),product(X2,product(X3,X1))) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005')).
% 3.58/3.99 cnf('0.32.1.0',plain,
% 3.58/3.99 ( quotient(quotient(product(X1,product(X2,X3)),X3),X2) = difference(product(X2,X3),product(X2,product(X3,X1))) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.32.0.0']),
% 3.58/3.99 [weight('<31,0,0,[0,0,0,32]>')]).
% 3.58/3.99 cnf('0.32.1.1',plain,
% 3.58/3.99 ( quotient(difference(X3,product(product(X3,X1),X2)),X2) = difference(product(X2,X3),product(X2,product(X3,X1))) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.32.1.0','0.31.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.32.2.0',plain,
% 3.58/3.99 ( quotient(difference(X1,product(product(X1,X2),X3)),X3) = difference(product(X3,X1),product(X3,product(X1,X2))) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.32.1.1',theory(equality)]),
% 3.58/3.99 [u,rule_32]).
% 3.58/3.99 cnf('0.40.0.0',plain,
% 3.58/3.99 ( one = difference(X1,X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.40.1.0',plain,
% 3.58/3.99 ( one = difference(X1,X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.40.0.0']),
% 3.58/3.99 [weight('<19,6,2,[1,0,0,2]>')]).
% 3.58/3.99 cnf('0.40.2.0',plain,
% 3.58/3.99 ( difference(X1,X1) = one ),
% 3.58/3.99 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_40]).
% 3.58/3.99 cnf('0.44.0.0',plain,
% 3.58/3.99 ( one = product(j(X1),X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.3.2.0','0.25.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.44.1.0',plain,
% 3.58/3.99 ( one = product(j(X1),X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.44.0.0']),
% 3.58/3.99 [weight('<29,25,3,[0,0,0,1]>')]).
% 3.58/3.99 cnf('0.44.2.0',plain,
% 3.58/3.99 ( product(j(X1),X1) = one ),
% 3.58/3.99 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_44]).
% 3.58/3.99 cnf('0.45.0.0',plain,
% 3.58/3.99 ( X1 = difference(j(X1),one) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.6.2.0','0.44.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.45.0.1',plain,
% 3.58/3.99 ( X1 = i(j(X1)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.45.0.0','0.29.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.45.1.0',plain,
% 3.58/3.99 ( X1 = i(j(X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.45.0.1']),
% 3.58/3.99 [weight('<19,44,6,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.45.2.0',plain,
% 3.58/3.99 ( i(j(X1)) = X1 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_45]).
% 3.58/3.99 cnf('0.46.0.0',plain,
% 3.58/3.99 ( one = product(X1,i(X1)) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.1.2.0','0.29.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.46.1.0',plain,
% 3.58/3.99 ( one = product(X1,i(X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.46.0.0']),
% 3.58/3.99 [weight('<29,29,1,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.46.2.0',plain,
% 3.58/3.99 ( product(X1,i(X1)) = one ),
% 3.58/3.99 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_46]).
% 3.58/3.99 cnf('0.54.0.0',plain,
% 3.58/3.99 ( product(j(j(X1)),one) = product(X1,eta(X1)) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.11.2.0','0.2.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.54.0.1',plain,
% 3.58/3.99 ( j(j(X1)) = product(X1,eta(X1)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.54.0.0','0.2.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.54.1.0',plain,
% 3.58/3.99 ( j(j(X1)) = product(X1,eta(X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.54.0.1']),
% 3.58/3.99 [weight('<39,11,2,[1,0,0,2]>')]).
% 3.58/3.99 cnf('0.54.2.0',plain,
% 3.58/3.99 ( product(X1,eta(X1)) = j(j(X1)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_54]).
% 3.58/3.99 cnf('0.88.0.0',plain,
% 3.58/3.99 ( a(X1,X2,j(X3)) = a(X3,X1,X2) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.28.2.0','0.45.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.88.1.0',plain,
% 3.58/3.99 ( a(X1,X2,j(X3)) = a(X3,X1,X2) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.88.0.0']),
% 3.58/3.99 [weight('<59,45,28,[0,0,0,1]>')]).
% 3.58/3.99 cnf('0.88.2.0',plain,
% 3.58/3.99 ( a(X1,X2,j(X3)) = a(X3,X1,X2) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.88.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_88]).
% 3.58/3.99 cnf('0.98.0.0',plain,
% 3.58/3.99 ( difference(product(X1,X2),product(X1,product(X2,i(X2)))) = quotient(difference(X2,product(one,X1)),X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.32.2.0','0.46.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1.2.1','L')]).
% 3.58/3.99 cnf('0.98.0.1',plain,
% 3.58/3.99 ( difference(product(X1,X2),product(X1,one)) = quotient(difference(X2,product(one,X1)),X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.98.0.0','0.46.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2.2','L')]).
% 3.58/3.99 cnf('0.98.0.2',plain,
% 3.58/3.99 ( difference(product(X1,X2),X1) = quotient(difference(X2,product(one,X1)),X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.98.0.1','0.2.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.98.0.3',plain,
% 3.58/3.99 ( difference(product(X1,X2),X1) = quotient(difference(X2,X1),X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.98.0.2','0.4.2.0',theory(equality)]),
% 3.58/3.99 [pos('R.1.2','L')]).
% 3.58/3.99 cnf('0.98.1.0',plain,
% 3.58/3.99 ( difference(product(X1,X2),X1) = quotient(difference(X2,X1),X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.98.0.3']),
% 3.58/3.99 [weight('<65,46,32,[0,0,0,4]>')]).
% 3.58/3.99 cnf('0.98.2.0',plain,
% 3.58/3.99 ( quotient(difference(X1,X2),X2) = difference(product(X2,X1),X2) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_98]).
% 3.58/3.99 cnf('0.99.0.0',plain,
% 3.58/3.99 ( difference(product(X1,X1),X1) = quotient(one,X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.98.2.0','0.40.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.99.0.1',plain,
% 3.58/3.99 ( difference(product(X1,X1),X1) = j(X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.99.0.0','0.25.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.99.1.0',plain,
% 3.58/3.99 ( difference(product(X1,X1),X1) = j(X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.99.0.1']),
% 3.58/3.99 [weight('<47,98,40,[1,0,0,1]>')]).
% 3.58/3.99 cnf('0.99.2.0',plain,
% 3.58/3.99 ( difference(product(X1,X1),X1) = j(X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_99]).
% 3.58/3.99 cnf('0.101.0.0',plain,
% 3.58/3.99 ( X1 = product(product(X1,X1),j(X1)) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.1.2.0','0.99.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.101.1.0',plain,
% 3.58/3.99 ( X1 = product(product(X1,X1),j(X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.101.0.0']),
% 3.58/3.99 [weight('<55,99,1,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.101.2.0',plain,
% 3.58/3.99 ( product(product(X1,X1),j(X1)) = X1 ),
% 3.58/3.99 inference(orient,[status(thm)],['0.101.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_101]).
% 3.58/3.99 cnf('0.244.0.0',plain,
% 3.58/3.99 ( a(X1,X2,X3) = product(a(X1,X2,X3),product(a(X1,X2,X3),j(a(X1,X2,X3)))) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.101.2.0','0.15.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.244.0.1',plain,
% 3.58/3.99 ( a(X1,X2,X3) = product(a(X1,X2,X3),eta(a(X1,X2,X3))) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.244.0.0','0.21.2.0',theory(equality)]),
% 3.58/3.99 [pos('R.2','L')]).
% 3.58/3.99 cnf('0.244.0.2',plain,
% 3.58/3.99 ( a(X1,X2,X3) = j(j(a(X1,X2,X3))) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.244.0.1','0.54.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.244.1.0',plain,
% 3.58/3.99 ( a(X1,X2,X3) = j(j(a(X1,X2,X3))) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.244.0.2']),
% 3.58/3.99 [weight('<76,101,15,[1,0,0,0]>')]).
% 3.58/3.99 cnf('0.244.2.0',plain,
% 3.58/3.99 ( j(j(a(X1,X2,X3))) = a(X1,X2,X3) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.244.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_244]).
% 3.58/3.99 cnf('0.246.0.0',plain,
% 3.58/3.99 ( j(a(X1,X2,X3)) = i(a(X1,X2,X3)) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.45.2.0','0.244.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.246.1.0',plain,
% 3.58/3.99 ( j(a(X1,X2,X3)) = i(a(X1,X2,X3)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.246.0.0']),
% 3.58/3.99 [weight('<65,244,45,[0,0,0,1]>')]).
% 3.58/3.99 cnf('0.246.2.0',plain,
% 3.58/3.99 ( j(a(X1,X2,X3)) = i(a(X1,X2,X3)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.246.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_246]).
% 3.58/3.99 cnf('0.1320.0.0',plain,
% 3.58/3.99 ( difference(X1,product(product(X1,X2),j(X1))) = quotient(product(X2,one),X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.31.2.0','0.44.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1.2','L')]).
% 3.58/3.99 cnf('0.1320.0.1',plain,
% 3.58/3.99 ( difference(X1,product(product(X1,X2),j(X1))) = quotient(X2,X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.1320.0.0','0.2.2.0',theory(equality)]),
% 3.58/3.99 [pos('R.1','L')]).
% 3.58/3.99 cnf('0.1320.1.0',plain,
% 3.58/3.99 ( difference(X1,product(product(X1,X2),j(X1))) = quotient(X2,X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.1320.0.1']),
% 3.58/3.99 [weight('<107,44,31,[0,0,0,3]>')]).
% 3.58/3.99 cnf('0.1320.2.0',plain,
% 3.58/3.99 ( difference(X1,product(product(X1,X2),j(X1))) = quotient(X2,X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.1320.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_1316]).
% 3.58/3.99 cnf('0.1321.0.0',plain,
% 3.58/3.99 ( product(product(X1,X2),j(X1)) = product(X1,quotient(X2,X1)) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.1.2.0','0.1320.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.1321.1.0',plain,
% 3.58/3.99 ( product(product(X1,X2),j(X1)) = product(X1,quotient(X2,X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.1321.0.0']),
% 3.58/3.99 [weight('<83,1320,1,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.1321.2.0',plain,
% 3.58/3.99 ( product(product(X1,X2),j(X1)) = product(X1,quotient(X2,X1)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.1321.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_1317]).
% 3.58/3.99 cnf('0.1835.0.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X4) = quotient(product(a(X1,X2,X3),product(X4,X5)),X5) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.5.2.0','0.15.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.1835.1.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X4) = quotient(product(a(X1,X2,X3),product(X4,X5)),X5) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.1835.0.0']),
% 3.58/3.99 [weight('<?,15,5,[0,0,0,1]>')]).
% 3.58/3.99 cnf('0.1835.1.1',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X4) = difference(X5,product(product(X5,a(X1,X2,X3)),X4)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.1835.1.0','0.31.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.1835.2.0',plain,
% 3.58/3.99 ( difference(X1,product(product(X1,a(X2,X3,X4)),X5)) = product(a(X2,X3,X4),X5) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.1835.1.1',theory(equality)]),
% 3.58/3.99 [x,rule_1828]).
% 3.58/3.99 cnf('0.2632.0.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),quotient(X4,a(X1,X2,X3))) = product(a(X1,X2,X3),product(X4,j(a(X1,X2,X3)))) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.1321.2.0','0.15.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.2632.0.1',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),quotient(X4,a(X1,X2,X3))) = product(a(X1,X2,X3),product(X4,i(a(X1,X2,X3)))) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2632.0.0','0.246.2.0',theory(equality)]),
% 3.58/3.99 [pos('R.2.2','L')]).
% 3.58/3.99 cnf('0.2632.1.0',plain,
% 3.58/3.99 ( quotient(X4,a(X1,X2,X3)) = product(X4,i(a(X1,X2,X3))) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2632.0.1']),
% 3.58/3.99 [weight('<111,1321,15,[1,0,0,0]>')]).
% 3.58/3.99 cnf('0.2632.2.0',plain,
% 3.58/3.99 ( product(X1,i(a(X2,X3,X4))) = quotient(X1,a(X2,X3,X4)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2632.1.0',theory(equality)]),
% 3.58/3.99 [x,rule_2621]).
% 3.58/3.99 cnf('0.2776.0.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),j(X4)) = difference(X4,product(X4,quotient(a(X1,X2,X3),X4))) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.1835.2.0','0.1321.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.2776.0.1',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),j(X4)) = quotient(a(X1,X2,X3),X4) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2776.0.0','0.6.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.2776.1.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),j(X4)) = quotient(a(X1,X2,X3),X4) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2776.0.1']),
% 3.58/3.99 [weight('<111,1835,1321,[1,0,0,2]>')]).
% 3.58/3.99 cnf('0.2776.2.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),j(X4)) = quotient(a(X1,X2,X3),X4) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2776.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_2761]).
% 3.58/3.99 cnf('0.2946.0.0',plain,
% 3.58/3.99 ( difference(X1,product(a(X1,X2,X3),X1)) = difference(a(X2,X3,X1),one) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.6.2.0','0.20.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.2946.1.0',plain,
% 3.58/3.99 ( difference(X1,product(a(X1,X2,X3),X1)) = difference(a(X2,X3,X1),one) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2946.0.0']),
% 3.58/3.99 [weight('<?,20,6,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.2946.1.1',plain,
% 3.58/3.99 ( difference(X1,product(a(X1,X2,X3),X1)) = i(a(X2,X3,X1)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2946.1.0','0.29.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.2946.2.0',plain,
% 3.58/3.99 ( difference(X1,product(a(X1,X2,X3),X1)) = i(a(X2,X3,X1)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2946.1.1',theory(equality)]),
% 3.58/3.99 [u,rule_2929]).
% 3.58/3.99 cnf('0.2950.0.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X1) = product(X1,i(a(X2,X3,X1))) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.1.2.0','0.2946.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.2950.0.1',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X1) = quotient(X1,a(X2,X3,X1)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2950.0.0','0.2632.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.2950.1.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X1) = quotient(X1,a(X2,X3,X1)) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2950.0.1']),
% 3.58/3.99 [weight('<90,2946,1,[0,0,0,2]>')]).
% 3.58/3.99 cnf('0.2950.2.0',plain,
% 3.58/3.99 ( product(a(X1,X2,X3),X1) = quotient(X1,a(X2,X3,X1)) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2950.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_2933]).
% 3.58/3.99 cnf('0.2989.0.0',plain,
% 3.58/3.99 ( quotient(j(X1),a(X2,X3,j(X1))) = product(a(X2,X3,X1),j(X1)) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.2950.2.0','0.26.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.2989.0.1',plain,
% 3.58/3.99 ( quotient(j(X1),a(X1,X2,X3)) = product(a(X2,X3,X1),j(X1)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2989.0.0','0.88.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.2989.0.2',plain,
% 3.58/3.99 ( quotient(j(X1),a(X1,X2,X3)) = quotient(a(X2,X3,X1),X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2989.0.1','0.2776.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.2989.1.0',plain,
% 3.58/3.99 ( quotient(j(X1),a(X1,X2,X3)) = quotient(a(X2,X3,X1),X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2989.0.2']),
% 3.58/3.99 [weight('<111,2950,26,[1,0,0,1]>')]).
% 3.58/3.99 cnf('0.2989.2.0',plain,
% 3.58/3.99 ( quotient(j(X1),a(X1,X2,X3)) = quotient(a(X2,X3,X1),X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2989.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_2972]).
% 3.58/3.99 cnf('0.2990.0.0',plain,
% 3.58/3.99 ( quotient(X1,a(X2,j(X3),X1)) = product(a(X3,X1,X2),X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.2950.2.0','0.88.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.2990.0.1',plain,
% 3.58/3.99 ( quotient(X1,a(X2,i(X3),X1)) = product(a(X3,X1,X2),X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2990.0.0','0.27.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.2990.1.0',plain,
% 3.58/3.99 ( quotient(X1,a(X2,i(X3),X1)) = product(a(X3,X1,X2),X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2990.0.1']),
% 3.58/3.99 [weight('<111,2950,88,[1,0,0,1]>')]).
% 3.58/3.99 cnf('0.2990.2.0',plain,
% 3.58/3.99 ( quotient(X1,a(X2,i(X3),X1)) = product(a(X3,X1,X2),X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2990.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_2973]).
% 3.58/3.99 cnf('0.2991.0.0',plain,
% 3.58/3.99 ( product(a(X1,j(X2),X2),j(X2)) = quotient(a(i(X1),j(X2),X2),X2) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.2990.2.0','0.2989.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.2991.0.1',plain,
% 3.58/3.99 ( quotient(a(X1,j(X2),X2),X2) = quotient(a(i(X1),j(X2),X2),X2) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2991.0.0','0.2776.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.2991.0.2',plain,
% 3.58/3.99 ( quotient(a(X1,i(X2),X2),X2) = quotient(a(i(X1),j(X2),X2),X2) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2991.0.1','0.27.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.2991.0.3',plain,
% 3.58/3.99 ( quotient(a(X1,i(X2),X2),X2) = quotient(a(j(X2),X2,X1),X2) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2991.0.2','0.28.2.0',theory(equality)]),
% 3.58/3.99 [pos('R.1','L')]).
% 3.58/3.99 cnf('0.2991.0.4',plain,
% 3.58/3.99 ( quotient(a(X1,i(X2),X2),X2) = quotient(a(X2,X1,X2),X2) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2991.0.3','0.26.2.0',theory(equality)]),
% 3.58/3.99 [pos('R.1','L')]).
% 3.58/3.99 cnf('0.2991.1.0',plain,
% 3.58/3.99 ( a(X1,i(X2),X2) = a(X2,X1,X2) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2991.0.4']),
% 3.58/3.99 [weight('<59,2990,2989,[1,0,0,0]>')]).
% 3.58/3.99 cnf('0.2991.2.0',plain,
% 3.58/3.99 ( a(X1,i(X2),X2) = a(X2,X1,X2) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2991.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_2974]).
% 3.58/3.99 cnf('0.2992.0.0',plain,
% 3.58/3.99 ( a(X1,j(X2),X1) = a(i(X1),X1,X2) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.2991.2.0','0.26.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.2992.0.1',plain,
% 3.58/3.99 ( a(X1,i(X2),X1) = a(i(X1),X1,X2) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2992.0.0','0.27.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','L')]).
% 3.58/3.99 cnf('0.2992.0.2',plain,
% 3.58/3.99 ( a(X1,i(X2),X1) = a(X1,X2,X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2992.0.1','0.28.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.2992.1.0',plain,
% 3.58/3.99 ( a(X1,i(X2),X1) = a(X1,X2,X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2992.0.2']),
% 3.58/3.99 [weight('<59,2991,26,[1,0,0,0]>')]).
% 3.58/3.99 cnf('0.2992.2.0',plain,
% 3.58/3.99 ( a(X1,i(X2),X1) = a(X1,X2,X1) ),
% 3.58/3.99 inference(orient,[status(thm)],['0.2992.1.0',theory(equality)]),
% 3.58/3.99 [u,rule_2975]).
% 3.58/3.99 cnf('0.2993.0.0',plain,
% 3.58/3.99 ( quotient(X1,a(i(X2),X1,X1)) = product(a(X1,X2,X1),X1) ),
% 3.58/3.99 inference(cp,[status(thm)],['0.2950.2.0','0.2992.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.1','L')]).
% 3.58/3.99 cnf('0.2993.0.1',plain,
% 3.58/3.99 ( quotient(X1,a(X1,X1,X2)) = product(a(X1,X2,X1),X1) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2993.0.0','0.28.2.0',theory(equality)]),
% 3.58/3.99 [pos('L.2','L')]).
% 3.58/3.99 cnf('0.2993.0.2',plain,
% 3.58/3.99 ( quotient(X1,a(X1,X1,X2)) = quotient(X1,a(X2,X1,X1)) ),
% 3.58/3.99 inference(reduction,[status(thm)],['0.2993.0.1','0.2950.2.0',theory(equality)]),
% 3.58/3.99 [pos('R','L')]).
% 3.58/3.99 cnf('0.2993.1.0',plain,
% 3.58/3.99 ( a(X1,X1,X2) = a(X2,X1,X1) ),
% 3.58/3.99 inference(weigh,[status(thm)],['0.2993.0.2']),
% 3.58/3.99 [weight('<80,2992,2950,[0,0,0,1]>')]).
% 3.58/3.99 cnf('0.2993.2.0',plain,
% 3.58/3.99 ( a(X1,X1,X2) = a(X2,X1,X1) ),
% 3.58/3.99 inference(activate,[status(thm)],['0.2993.1.0']),
% 3.58/3.99 [equation_18]).
% 3.58/3.99 cnf('1.0.0.0',conjecture,
% 3.58/3.99 ( a(x0,x1,x1) = a(x1,x1,x0) ),
% 3.58/3.99 file('/tmp/WALDMEISTER_4557_n005',conjecture_1)).
% 3.58/3.99 cnf('1.0.0.1',plain,
% 3.58/3.99 ( a(x1,x1,x0) = a(x1,x1,x0) ),
% 3.58/3.99 inference(reduction,[status(thm)],['1.0.0.0','0.2993.2.0',theory(equality)]),
% 3.58/3.99 [pos('L','R')]).
% 3.58/3.99 cnf('1.0.0.2',plain,
% 3.58/3.99 ( $true ),
% 3.58/3.99 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 3.58/3.99 [conjecture_1]).
% 3.58/3.99
% 3.58/3.99 Proved Goals:
% 3.58/3.99 No. 1: a(x0,x1,x1) ?= a(x1,x1,x0) joined, current: a(x1,x1,x0) = a(x1,x1,x0)
% 3.58/3.99 1 goal was specified, which was proved.
% 3.58/3.99 % SZS output end CNFRefutation
% 3.58/3.99 #END OF PROOF
% 3.58/3.99
% 3.58/3.99 Problem WALDMEISTER_4557_n005
% 3.58/3.99 CPs.gen 1561178
% 3.58/3.99 CPs.reexp 0
% 3.58/3.99 Select 20472
% 3.58/3.99 R 2975
% 3.58/3.99 E 18
% 3.58/3.99 vsize 10.1M
% 3.58/3.99 rss 5.7M
% 3.58/3.99 process.time 2.983s
% 3.58/3.99 wallclock.time 2.983s
% 3.58/3.99 status S
% 3.58/3.99
% 3.58/3.99
% 3.58/3.99 Waldmeister states: Goal proved.
% 3.58/3.99 % SZS status Unsatisfiable
%------------------------------------------------------------------------------