TSTP Solution File: GRP729-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP729-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n008.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 12:28:17 EDT 2022
% Result : Unsatisfiable 1.30s 1.72s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP729-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 07:28:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.96 ********************************************************************************
% 0.59/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.96 * |/ | \/ | *
% 0.59/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.96 * A. Jaeger and B. Loechner | | *
% 0.59/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.96 ********************************************************************************
% 0.59/0.96
% 0.59/0.96
% 0.59/0.96 Goals:
% 0.59/0.96 ------
% 0.59/0.96
% 0.59/0.96 ( 1) unit ?=? asoc(a,b,op_k(c,d))
% 0.59/0.96
% 0.59/0.96 Detected structure: Praeloop
% 0.59/0.96 ********************************************************************************
% 0.59/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.96 ********************************************************************************
% 0.59/0.96
% 1.30/1.72 joined goal: 1 unit ?= asoc(a,b,op_k(c,d)) to unit
% 1.30/1.72 goal joined
% 1.30/1.72 % SZS status Unsatisfiable
% 1.30/1.72 #START OF PROOF
% 1.30/1.72 % SZS output start CNFRefutation
% 1.30/1.72 cnf('0.1.0.0',axiom,
% 1.30/1.72 ( X1 = mult(X1,unit) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.1.1.0',plain,
% 1.30/1.72 ( X1 = mult(X1,unit) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.30/1.72 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.30/1.72 cnf('0.1.2.0',plain,
% 1.30/1.72 ( mult(X1,unit) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_1]).
% 1.30/1.72 cnf('0.2.0.0',axiom,
% 1.30/1.72 ( X1 = mult(i(X2),mult(X2,X1)) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.2.1.0',plain,
% 1.30/1.72 ( X1 = mult(i(X2),mult(X2,X1)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.30/1.72 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.30/1.72 cnf('0.2.2.0',plain,
% 1.30/1.72 ( mult(i(X1),mult(X1,X2)) = X2 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_2]).
% 1.30/1.72 cnf('0.3.0.0',axiom,
% 1.30/1.72 ( X1 = mult(unit,X1) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.3.1.0',plain,
% 1.30/1.72 ( X1 = mult(unit,X1) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.30/1.72 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.3.2.0',plain,
% 1.30/1.72 ( mult(unit,X1) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_3]).
% 1.30/1.72 cnf('0.4.0.0',axiom,
% 1.30/1.72 ( X1 = mult(rd(X1,X2),X2) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.4.1.0',plain,
% 1.30/1.72 ( X1 = mult(rd(X1,X2),X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.30/1.72 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.30/1.72 cnf('0.4.2.0',plain,
% 1.30/1.72 ( mult(rd(X1,X2),X2) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_4]).
% 1.30/1.72 cnf('0.5.0.0',axiom,
% 1.30/1.72 ( X1 = rd(mult(X1,X2),X2) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.5.1.0',plain,
% 1.30/1.72 ( X1 = rd(mult(X1,X2),X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.30/1.72 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.30/1.72 cnf('0.5.2.0',plain,
% 1.30/1.72 ( rd(mult(X1,X2),X2) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_5]).
% 1.30/1.72 cnf('0.6.0.0',axiom,
% 1.30/1.72 ( mult(X1,X2) = mult(mult(X2,X1),op_k(X1,X2)) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.6.1.0',plain,
% 1.30/1.72 ( mult(X1,X2) = mult(mult(X2,X1),op_k(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.6.0.0']),
% 1.30/1.72 [weight('<5,0,0,[0,0,0,6]>')]).
% 1.30/1.72 cnf('0.6.2.0',plain,
% 1.30/1.72 ( mult(mult(X1,X2),op_k(X2,X1)) = mult(X2,X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_6]).
% 1.30/1.72 cnf('0.9.0.0',axiom,
% 1.30/1.72 ( mult(mult(X1,X2),X3) = mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.9.1.0',plain,
% 1.30/1.72 ( mult(mult(X1,X2),X3) = mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.9.0.0']),
% 1.30/1.72 [weight('<8,0,0,[0,0,0,9]>')]).
% 1.30/1.72 cnf('0.9.2.0',plain,
% 1.30/1.72 ( mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)) = mult(mult(X1,X2),X3) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_9]).
% 1.30/1.72 cnf('0.10.0.0',axiom,
% 1.30/1.72 ( mult(i(X1),X1) = unit ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.10.1.0',plain,
% 1.30/1.72 ( mult(i(X1),X1) = unit ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.10.0.0']),
% 1.30/1.72 [weight('<9,0,0,[0,0,0,10]>')]).
% 1.30/1.72 cnf('0.10.2.0',plain,
% 1.30/1.72 ( mult(i(X1),X1) = unit ),
% 1.30/1.72 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_10]).
% 1.30/1.72 cnf('0.11.0.0',axiom,
% 1.30/1.72 ( mult(i(X1),mult(X2,X1)) = op_t(X2,X1) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.11.1.0',plain,
% 1.30/1.72 ( mult(i(X1),mult(X2,X1)) = op_t(X2,X1) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.11.0.0']),
% 1.30/1.72 [weight('<10,0,0,[0,0,0,11]>')]).
% 1.30/1.72 cnf('0.11.2.0',plain,
% 1.30/1.72 ( mult(i(X1),mult(X2,X1)) = op_t(X2,X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_11]).
% 1.30/1.72 cnf('0.12.0.0',axiom,
% 1.30/1.72 ( mult(i(X1),i(X2)) = i(mult(X1,X2)) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.12.1.0',plain,
% 1.30/1.72 ( mult(i(X1),i(X2)) = i(mult(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.12.0.0']),
% 1.30/1.72 [weight('<11,0,0,[0,0,0,12]>')]).
% 1.30/1.72 cnf('0.12.2.0',plain,
% 1.30/1.72 ( mult(i(X1),i(X2)) = i(mult(X1,X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_12]).
% 1.30/1.72 cnf('0.14.0.0',axiom,
% 1.30/1.72 ( op_t(op_t(X1,X2),X3) = op_t(op_t(X1,X3),X2) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.14.1.0',plain,
% 1.30/1.72 ( op_t(op_t(X1,X2),X3) = op_t(op_t(X1,X3),X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.14.0.0']),
% 1.30/1.72 [weight('<13,0,0,[0,0,0,14]>')]).
% 1.30/1.72 cnf('0.14.2.0',plain,
% 1.30/1.72 ( op_t(op_t(X1,X2),X3) = op_t(op_t(X1,X3),X2) ),
% 1.30/1.72 inference(activate,[status(thm)],['0.14.1.0']),
% 1.30/1.72 [equation_1]).
% 1.30/1.72 cnf('0.21.0.0',axiom,
% 1.30/1.72 ( unit = asoc(X1,X2,asoc(X3,X4,X5)) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008')).
% 1.30/1.72 cnf('0.21.1.0',plain,
% 1.30/1.72 ( unit = asoc(X1,X2,asoc(X3,X4,X5)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.21.0.0']),
% 1.30/1.72 [weight('<20,0,0,[0,0,0,21]>')]).
% 1.30/1.72 cnf('0.21.2.0',plain,
% 1.30/1.72 ( asoc(X1,X2,asoc(X3,X4,X5)) = unit ),
% 1.30/1.72 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_18]).
% 1.30/1.72 cnf('0.26.0.0',plain,
% 1.30/1.72 ( X1 = mult(i(i(X1)),unit) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.2.2.0','0.10.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.26.0.1',plain,
% 1.30/1.72 ( X1 = i(i(X1)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.26.0.0','0.1.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.26.1.0',plain,
% 1.30/1.72 ( X1 = i(i(X1)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.26.0.1']),
% 1.30/1.72 [weight('<19,10,2,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.26.2.0',plain,
% 1.30/1.72 ( i(i(X1)) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_23]).
% 1.30/1.72 cnf('0.41.0.0',plain,
% 1.30/1.72 ( op_t(i(X1),X1) = mult(i(X1),unit) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.11.2.0','0.10.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.41.0.1',plain,
% 1.30/1.72 ( op_t(i(X1),X1) = i(X1) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.41.0.0','0.1.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.41.1.0',plain,
% 1.30/1.72 ( op_t(i(X1),X1) = i(X1) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.41.0.1']),
% 1.30/1.72 [weight('<34,11,10,[1,0,0,3]>')]).
% 1.30/1.72 cnf('0.41.2.0',plain,
% 1.30/1.72 ( op_t(i(X1),X1) = i(X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_38]).
% 1.30/1.72 cnf('0.42.0.0',plain,
% 1.30/1.72 ( i(i(X1)) = op_t(X1,i(X1)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.41.2.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.42.0.1',plain,
% 1.30/1.72 ( X1 = op_t(X1,i(X1)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.42.0.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L','L')]).
% 1.30/1.72 cnf('0.42.1.0',plain,
% 1.30/1.72 ( X1 = op_t(X1,i(X1)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.42.0.1']),
% 1.30/1.72 [weight('<29,41,26,[1,0,0,1]>')]).
% 1.30/1.72 cnf('0.42.2.0',plain,
% 1.30/1.72 ( op_t(X1,i(X1)) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_39]).
% 1.30/1.72 cnf('0.47.0.0',plain,
% 1.30/1.72 ( i(X1) = rd(X2,mult(X1,X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.47.1.0',plain,
% 1.30/1.72 ( i(X1) = rd(X2,mult(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.47.0.0']),
% 1.30/1.72 [weight('<47,5,2,[1,0,0,1]>')]).
% 1.30/1.72 cnf('0.47.2.0',plain,
% 1.30/1.72 ( rd(X1,mult(X2,X1)) = i(X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_44]).
% 1.30/1.72 cnf('0.48.0.0',plain,
% 1.30/1.72 ( i(rd(X1,X2)) = rd(X2,X1) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.47.2.0','0.4.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.48.1.0',plain,
% 1.30/1.72 ( i(rd(X1,X2)) = rd(X2,X1) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.48.0.0']),
% 1.30/1.72 [weight('<39,47,4,[1,0,0,2]>')]).
% 1.30/1.72 cnf('0.48.2.0',plain,
% 1.30/1.72 ( i(rd(X1,X2)) = rd(X2,X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_45]).
% 1.30/1.72 cnf('0.50.0.0',plain,
% 1.30/1.72 ( X1 = mult(X2,mult(i(X2),X1)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.2.2.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.50.1.0',plain,
% 1.30/1.72 ( X1 = mult(X2,mult(i(X2),X1)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.50.0.0']),
% 1.30/1.72 [weight('<55,26,2,[0,0,0,1]>')]).
% 1.30/1.72 cnf('0.50.2.0',plain,
% 1.30/1.72 ( mult(X1,mult(i(X1),X2)) = X2 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_47]).
% 1.30/1.72 cnf('0.53.0.0',plain,
% 1.30/1.72 ( mult(X1,X2) = mult(X2,op_t(X1,X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.50.2.0','0.11.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.53.1.0',plain,
% 1.30/1.72 ( mult(X1,X2) = mult(X2,op_t(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.53.0.0']),
% 1.30/1.72 [weight('<53,50,11,[1,0,0,2]>')]).
% 1.30/1.72 cnf('0.53.2.0',plain,
% 1.30/1.72 ( mult(X1,op_t(X2,X1)) = mult(X2,X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_50]).
% 1.30/1.72 cnf('0.54.0.0',plain,
% 1.30/1.72 ( op_t(rd(X1,X2),X2) = mult(i(X2),X1) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.11.2.0','0.4.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.54.1.0',plain,
% 1.30/1.72 ( op_t(rd(X1,X2),X2) = mult(i(X2),X1) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.54.0.0']),
% 1.30/1.72 [weight('<59,11,4,[1,0,0,3]>')]).
% 1.30/1.72 cnf('0.54.2.0',plain,
% 1.30/1.72 ( op_t(rd(X1,X2),X2) = mult(i(X2),X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_51]).
% 1.30/1.72 cnf('0.55.0.0',plain,
% 1.30/1.72 ( op_t(i(X1),i(X2)) = mult(i(i(X2)),i(mult(X1,X2))) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.11.2.0','0.12.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.55.0.1',plain,
% 1.30/1.72 ( op_t(i(X1),i(X2)) = i(mult(i(X2),mult(X1,X2))) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.55.0.0','0.12.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.55.0.2',plain,
% 1.30/1.72 ( op_t(i(X1),i(X2)) = i(op_t(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.55.0.1','0.11.2.0',theory(equality)]),
% 1.30/1.72 [pos('R.1','L')]).
% 1.30/1.72 cnf('0.55.1.0',plain,
% 1.30/1.72 ( op_t(i(X1),i(X2)) = i(op_t(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.55.0.2']),
% 1.30/1.72 [weight('<59,12,11,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.55.2.0',plain,
% 1.30/1.72 ( op_t(i(X1),i(X2)) = i(op_t(X1,X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_52]).
% 1.30/1.72 cnf('0.57.0.0',plain,
% 1.30/1.72 ( i(mult(i(X1),X2)) = mult(X1,i(X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.12.2.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.57.1.0',plain,
% 1.30/1.72 ( i(mult(i(X1),X2)) = mult(X1,i(X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.57.0.0']),
% 1.30/1.72 [weight('<59,26,12,[0,0,0,1]>')]).
% 1.30/1.72 cnf('0.57.2.0',plain,
% 1.30/1.72 ( i(mult(i(X1),X2)) = mult(X1,i(X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_54]).
% 1.30/1.72 cnf('0.58.0.0',plain,
% 1.30/1.72 ( i(mult(X1,i(X2))) = mult(i(X1),X2) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.12.2.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.58.1.0',plain,
% 1.30/1.72 ( i(mult(X1,i(X2))) = mult(i(X1),X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.58.0.0']),
% 1.30/1.72 [weight('<59,26,12,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.58.2.0',plain,
% 1.30/1.72 ( i(mult(X1,i(X2))) = mult(i(X1),X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_55]).
% 1.30/1.72 cnf('0.59.0.0',plain,
% 1.30/1.72 ( i(op_t(i(X1),X2)) = op_t(X1,i(X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.55.2.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.59.1.0',plain,
% 1.30/1.72 ( i(op_t(i(X1),X2)) = op_t(X1,i(X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.59.0.0']),
% 1.30/1.72 [weight('<59,55,26,[1,0,0,1]>')]).
% 1.30/1.72 cnf('0.59.2.0',plain,
% 1.30/1.72 ( i(op_t(i(X1),X2)) = op_t(X1,i(X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_56]).
% 1.30/1.72 cnf('0.60.0.0',plain,
% 1.30/1.72 ( i(op_t(X1,i(X2))) = op_t(i(X1),X2) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.55.2.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.60.1.0',plain,
% 1.30/1.72 ( i(op_t(X1,i(X2))) = op_t(i(X1),X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.60.0.0']),
% 1.30/1.72 [weight('<59,55,26,[1,0,0,3]>')]).
% 1.30/1.72 cnf('0.60.2.0',plain,
% 1.30/1.72 ( i(op_t(X1,i(X2))) = op_t(i(X1),X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_57]).
% 1.30/1.72 cnf('0.61.0.0',plain,
% 1.30/1.72 ( i(X1) = mult(X2,i(mult(X2,X1))) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.50.2.0','0.12.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.61.1.0',plain,
% 1.30/1.72 ( i(X1) = mult(X2,i(mult(X2,X1))) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.61.0.0']),
% 1.30/1.72 [weight('<62,50,12,[1,0,0,2]>')]).
% 1.30/1.72 cnf('0.61.2.0',plain,
% 1.30/1.72 ( mult(X1,i(mult(X1,X2))) = i(X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_58]).
% 1.30/1.72 cnf('0.71.0.0',plain,
% 1.30/1.72 ( op_t(op_t(X1,X2),i(X1)) = op_t(X1,X2) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.14.2.0','0.42.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.71.1.0',plain,
% 1.30/1.72 ( op_t(op_t(X1,X2),i(X1)) = op_t(X1,X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.71.0.0']),
% 1.30/1.72 [weight('<69,42,14,[0,0,0,1]>')]).
% 1.30/1.72 cnf('0.71.2.0',plain,
% 1.30/1.72 ( op_t(op_t(X1,X2),i(X1)) = op_t(X1,X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_68]).
% 1.30/1.72 cnf('0.81.0.0',plain,
% 1.30/1.72 ( mult(X1,i(mult(X2,X1))) = i(op_t(X2,X1)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.57.2.0','0.11.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.81.1.0',plain,
% 1.30/1.72 ( mult(X1,i(mult(X2,X1))) = i(op_t(X2,X1)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.81.0.0']),
% 1.30/1.72 [weight('<76,57,11,[1,0,0,1]>')]).
% 1.30/1.72 cnf('0.81.2.0',plain,
% 1.30/1.72 ( mult(X1,i(mult(X2,X1))) = i(op_t(X2,X1)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.81.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_78]).
% 1.30/1.72 cnf('0.82.0.0',plain,
% 1.30/1.72 ( op_t(i(rd(X1,i(X2))),X2) = i(mult(i(i(X2)),X1)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.60.2.0','0.54.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.82.0.1',plain,
% 1.30/1.72 ( op_t(rd(i(X2),X1),X2) = i(mult(i(i(X2)),X1)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.82.0.0','0.48.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.82.0.2',plain,
% 1.30/1.72 ( op_t(rd(i(X2),X1),X2) = mult(i(X2),i(X1)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.82.0.1','0.57.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.82.0.3',plain,
% 1.30/1.72 ( op_t(rd(i(X2),X1),X2) = i(mult(X2,X1)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.82.0.2','0.12.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.82.1.0',plain,
% 1.30/1.72 ( op_t(rd(i(X2),X1),X2) = i(mult(X2,X1)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.82.0.3']),
% 1.30/1.72 [weight('<76,60,54,[1,0,0,1]>')]).
% 1.30/1.72 cnf('0.82.2.0',plain,
% 1.30/1.72 ( op_t(rd(i(X1),X2),X1) = i(mult(X1,X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.82.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_79]).
% 1.30/1.72 cnf('0.113.0.0',plain,
% 1.30/1.72 ( op_k(X1,X2) = mult(i(mult(X2,X1)),mult(X1,X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.2.2.0','0.6.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.113.1.0',plain,
% 1.30/1.72 ( op_k(X1,X2) = mult(i(mult(X2,X1)),mult(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.113.0.0']),
% 1.30/1.72 [weight('<?,6,2,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.113.2.0',plain,
% 1.30/1.72 ( mult(i(mult(X1,X2)),mult(X2,X1)) = op_k(X2,X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.113.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_108]).
% 1.30/1.72 cnf('0.152.0.0',plain,
% 1.30/1.72 ( mult(op_t(X1,X2),i(X1)) = mult(i(X1),op_t(X1,X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.53.2.0','0.71.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.152.1.0',plain,
% 1.30/1.72 ( mult(op_t(X1,X2),i(X1)) = mult(i(X1),op_t(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.152.0.0']),
% 1.30/1.72 [weight('<90,71,53,[0,0,0,2]>')]).
% 1.30/1.72 cnf('0.152.2.0',plain,
% 1.30/1.72 ( mult(op_t(X1,X2),i(X1)) = mult(i(X1),op_t(X1,X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.152.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_147]).
% 1.30/1.72 cnf('0.153.0.0',plain,
% 1.30/1.72 ( i(i(X1)) = mult(op_t(X1,X2),i(mult(i(X1),op_t(X1,X2)))) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.61.2.0','0.152.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2.1','L')]).
% 1.30/1.72 cnf('0.153.0.1',plain,
% 1.30/1.72 ( X1 = mult(op_t(X1,X2),i(mult(i(X1),op_t(X1,X2)))) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.153.0.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('L','L')]).
% 1.30/1.72 cnf('0.153.0.2',plain,
% 1.30/1.72 ( X1 = i(op_t(i(X1),op_t(X1,X2))) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.153.0.1','0.81.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.153.0.3',plain,
% 1.30/1.72 ( X1 = op_t(X1,i(op_t(X1,X2))) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.153.0.2','0.59.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.153.1.0',plain,
% 1.30/1.72 ( X1 = op_t(X1,i(op_t(X1,X2))) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.153.0.3']),
% 1.30/1.72 [weight('<55,152,61,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.153.2.0',plain,
% 1.30/1.72 ( op_t(X1,i(op_t(X1,X2))) = X1 ),
% 1.30/1.72 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_148]).
% 1.30/1.72 cnf('0.290.0.0',plain,
% 1.30/1.72 ( op_t(op_t(rd(X1,X2),X3),X2) = op_t(mult(i(X2),X1),X3) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.14.2.0','0.54.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.290.1.0',plain,
% 1.30/1.72 ( op_t(op_t(rd(X1,X2),X3),X2) = op_t(mult(i(X2),X1),X3) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.290.0.0']),
% 1.30/1.72 [weight('<111,54,14,[0,0,0,1]>')]).
% 1.30/1.72 cnf('0.290.2.0',plain,
% 1.30/1.72 ( op_t(op_t(rd(X1,X2),X3),X2) = op_t(mult(i(X2),X1),X3) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.290.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_285]).
% 1.30/1.72 cnf('0.325.0.0',plain,
% 1.30/1.72 ( i(op_k(X1,X2)) = mult(mult(X2,X1),i(mult(X1,X2))) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.61.2.0','0.6.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2.1','L')]).
% 1.30/1.72 cnf('0.325.1.0',plain,
% 1.30/1.72 ( i(op_k(X1,X2)) = mult(mult(X2,X1),i(mult(X1,X2))) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.325.0.0']),
% 1.30/1.72 [weight('<116,61,6,[1,0,0,3]>')]).
% 1.30/1.72 cnf('0.325.2.0',plain,
% 1.30/1.72 ( mult(mult(X1,X2),i(mult(X2,X1))) = i(op_k(X2,X1)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.325.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_320]).
% 1.30/1.72 cnf('0.340.0.0',plain,
% 1.30/1.72 ( rd(i(X1),X2) = op_t(rd(i(X1),X2),i(i(mult(X1,X2)))) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.153.2.0','0.82.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2.1','L')]).
% 1.30/1.72 cnf('0.340.0.1',plain,
% 1.30/1.72 ( rd(i(X1),X2) = op_t(rd(i(X1),X2),mult(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.340.0.0','0.26.2.0',theory(equality)]),
% 1.30/1.72 [pos('R.2','L')]).
% 1.30/1.72 cnf('0.340.1.0',plain,
% 1.30/1.72 ( rd(i(X1),X2) = op_t(rd(i(X1),X2),mult(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.340.0.1']),
% 1.30/1.72 [weight('<116,153,82,[1,0,0,3]>')]).
% 1.30/1.72 cnf('0.340.2.0',plain,
% 1.30/1.72 ( op_t(rd(i(X1),X2),mult(X1,X2)) = rd(i(X1),X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.340.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_335]).
% 1.30/1.72 cnf('0.376.0.0',plain,
% 1.30/1.72 ( op_t(mult(i(X1),i(X2)),mult(X2,X1)) = op_t(rd(i(X2),X1),X1) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.290.2.0','0.340.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.376.0.1',plain,
% 1.30/1.72 ( op_t(i(mult(X1,X2)),mult(X2,X1)) = op_t(rd(i(X2),X1),X1) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.376.0.0','0.12.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.1','L')]).
% 1.30/1.72 cnf('0.376.0.2',plain,
% 1.30/1.72 ( op_t(i(mult(X1,X2)),mult(X2,X1)) = mult(i(X1),i(X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.376.0.1','0.54.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.376.0.3',plain,
% 1.30/1.72 ( op_t(i(mult(X1,X2)),mult(X2,X1)) = i(mult(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.376.0.2','0.12.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.376.1.0',plain,
% 1.30/1.72 ( op_t(i(mult(X1,X2)),mult(X2,X1)) = i(mult(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.376.0.3']),
% 1.30/1.72 [weight('<116,340,290,[0,0,0,1]>')]).
% 1.30/1.72 cnf('0.376.2.0',plain,
% 1.30/1.72 ( op_t(i(mult(X1,X2)),mult(X2,X1)) = i(mult(X1,X2)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.376.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_370]).
% 1.30/1.72 cnf('0.377.0.0',plain,
% 1.30/1.72 ( mult(i(mult(X1,X2)),mult(X2,X1)) = mult(mult(X2,X1),i(mult(X1,X2))) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.53.2.0','0.376.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.377.0.1',plain,
% 1.30/1.72 ( op_k(X2,X1) = mult(mult(X2,X1),i(mult(X1,X2))) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.377.0.0','0.113.2.0',theory(equality)]),
% 1.30/1.72 [pos('L','L')]).
% 1.30/1.72 cnf('0.377.0.2',plain,
% 1.30/1.72 ( op_k(X2,X1) = i(op_k(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.377.0.1','0.325.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.377.1.0',plain,
% 1.30/1.72 ( op_k(X2,X1) = i(op_k(X1,X2)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.377.0.2']),
% 1.30/1.72 [weight('<39,376,53,[0,0,0,2]>')]).
% 1.30/1.72 cnf('0.377.2.0',plain,
% 1.30/1.72 ( i(op_k(X1,X2)) = op_k(X2,X1) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.377.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_371]).
% 1.30/1.72 cnf('0.401.0.0',plain,
% 1.30/1.72 ( mult(mult(X1,X2),i(mult(X2,X1))) = i(op_k(X2,X1)) ),
% 1.30/1.72 inference(interreduction_right,[status(thm)],['0.325.2.0'])).
% 1.30/1.72 cnf('0.401.0.1',plain,
% 1.30/1.72 ( mult(mult(X1,X2),i(mult(X2,X1))) = op_k(X1,X2) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.401.0.0','0.377.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.401.1.0',plain,
% 1.30/1.72 ( mult(mult(X1,X2),i(mult(X2,X1))) = op_k(X1,X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.401.0.1']),
% 1.30/1.72 [weight('<107,325,377,[0,0,0,0]>')]).
% 1.30/1.72 cnf('0.401.2.0',plain,
% 1.30/1.72 ( mult(mult(X1,X2),i(mult(X2,X1))) = op_k(X1,X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.401.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_393]).
% 1.30/1.72 cnf('0.444.0.0',plain,
% 1.30/1.72 ( i(mult(X1,mult(X2,i(X3)))) = mult(i(X1),mult(i(X2),X3)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.12.2.0','0.58.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.444.1.0',plain,
% 1.30/1.72 ( i(mult(X1,mult(X2,i(X3)))) = mult(i(X1),mult(i(X2),X3)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.444.0.0']),
% 1.30/1.72 [weight('<119,58,12,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.444.2.0',plain,
% 1.30/1.72 ( i(mult(X1,mult(X2,i(X3)))) = mult(i(X1),mult(i(X2),X3)) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.444.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_436]).
% 1.30/1.72 cnf('0.1325.0.0',plain,
% 1.30/1.72 ( asoc(X1,X2,X3) = mult(i(mult(X1,mult(X2,X3))),mult(mult(X1,X2),X3)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.2.2.0','0.9.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.1325.1.0',plain,
% 1.30/1.72 ( asoc(X1,X2,X3) = mult(i(mult(X1,mult(X2,X3))),mult(mult(X1,X2),X3)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.1325.0.0']),
% 1.30/1.72 [weight('<?,9,2,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.1325.2.0',plain,
% 1.30/1.72 ( mult(i(mult(X1,mult(X2,X3))),mult(mult(X1,X2),X3)) = asoc(X1,X2,X3) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.1325.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_1317]).
% 1.30/1.72 cnf('0.1332.0.0',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = mult(i(mult(X1,mult(X2,i(mult(X2,X1))))),op_k(X1,X2)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.1325.2.0','0.401.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.2','L')]).
% 1.30/1.72 cnf('0.1332.0.1',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = mult(mult(i(X1),mult(i(X2),mult(X2,X1))),op_k(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.1332.0.0','0.444.2.0',theory(equality)]),
% 1.30/1.72 [pos('R.1','L')]).
% 1.30/1.72 cnf('0.1332.0.2',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = mult(mult(i(X1),X1),op_k(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.1332.0.1','0.2.2.0',theory(equality)]),
% 1.30/1.72 [pos('R.1.2','L')]).
% 1.30/1.72 cnf('0.1332.0.3',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = mult(unit,op_k(X1,X2)) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.1332.0.2','0.10.2.0',theory(equality)]),
% 1.30/1.72 [pos('R.1','L')]).
% 1.30/1.72 cnf('0.1332.0.4',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = op_k(X1,X2) ),
% 1.30/1.72 inference(reduction,[status(thm)],['0.1332.0.3','0.3.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('0.1332.1.0',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = op_k(X1,X2) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.1332.0.4']),
% 1.30/1.72 [weight('<87,1325,401,[1,0,0,7]>')]).
% 1.30/1.72 cnf('0.1332.2.0',plain,
% 1.30/1.72 ( asoc(X1,X2,i(mult(X2,X1))) = op_k(X1,X2) ),
% 1.30/1.72 inference(orient,[status(thm)],['0.1332.1.0',theory(equality)]),
% 1.30/1.72 [u,rule_1324]).
% 1.30/1.72 cnf('0.1337.0.0',plain,
% 1.30/1.72 ( unit = asoc(X1,X2,op_k(X3,X4)) ),
% 1.30/1.72 inference(cp,[status(thm)],['0.21.2.0','0.1332.2.0',theory(equality)]),
% 1.30/1.72 [pos('L.3','L')]).
% 1.30/1.72 cnf('0.1337.1.0',plain,
% 1.30/1.72 ( unit = asoc(X1,X2,op_k(X3,X4)) ),
% 1.30/1.72 inference(weigh,[status(thm)],['0.1337.0.0']),
% 1.30/1.72 [weight('<55,1332,21,[0,0,0,3]>')]).
% 1.30/1.72 cnf('0.1337.2.0',plain,
% 1.30/1.72 ( asoc(X1,X2,op_k(X3,X4)) = unit ),
% 1.30/1.72 inference(orient,[status(thm)],['0.1337.1.0',theory(equality)]),
% 1.30/1.72 [x,rule_1329]).
% 1.30/1.72 cnf('1.0.0.0',conjecture,
% 1.30/1.72 ( unit = asoc(a,b,op_k(c,d)) ),
% 1.30/1.72 file('/tmp/WALDMEISTER_10348_n008',conjecture_1)).
% 1.30/1.72 cnf('1.0.0.1',plain,
% 1.30/1.72 ( unit = unit ),
% 1.30/1.72 inference(reduction,[status(thm)],['1.0.0.0','0.1337.2.0',theory(equality)]),
% 1.30/1.72 [pos('R','L')]).
% 1.30/1.72 cnf('1.0.0.2',plain,
% 1.30/1.72 ( $true ),
% 1.30/1.72 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 1.30/1.72 [conjecture_1]).
% 1.30/1.72
% 1.30/1.72 Proved Goals:
% 1.30/1.72 No. 1: unit ?= asoc(a,b,op_k(c,d)) joined, current: unit = unit
% 1.30/1.72 1 goal was specified, which was proved.
% 1.30/1.72 % SZS output end CNFRefutation
% 1.30/1.72 #END OF PROOF
% 1.30/1.72
% 1.30/1.72 Problem WALDMEISTER_10348_n008
% 1.30/1.72 CPs.gen 353995
% 1.30/1.72 CPs.reexp 0
% 1.30/1.72 Select 7636
% 1.30/1.72 R 1329
% 1.30/1.72 E 8
% 1.30/1.72 vsize 9.0M
% 1.30/1.72 rss 4.7M
% 1.30/1.72 process.time 0.759s
% 1.30/1.72 wallclock.time 0.759s
% 1.30/1.72 status S
% 1.30/1.72
% 1.30/1.72
% 1.30/1.72 Waldmeister states: Goal proved.
% 1.30/1.72 % SZS status Unsatisfiable
%------------------------------------------------------------------------------