TSTP Solution File: GRP608-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP608-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:27:07 EDT 2022
% Result : Unsatisfiable 0.68s 1.04s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP608-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : woody %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 10:42:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.68/1.03 ********************************************************************************
% 0.68/1.03 * W A L D M E I S T E R \| \ / \|/ *
% 0.68/1.03 * |/ | \/ | *
% 0.68/1.03 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.68/1.03 * A. Jaeger and B. Loechner | | *
% 0.68/1.03 * <waldmeister@informatik.uni-kl.de> | *
% 0.68/1.03 ********************************************************************************
% 0.68/1.03
% 0.68/1.03
% 0.68/1.03 Goals:
% 0.68/1.03 ------
% 0.68/1.03
% 0.68/1.03 ( 1) multiply(a,b) ?=? multiply(b,a)
% 0.68/1.03
% 0.68/1.03 Detected structure: Orkus
% 0.68/1.03 ********************************************************************************
% 0.68/1.03 ****************************** COMPLETION - PROOF ******************************
% 0.68/1.03 ********************************************************************************
% 0.68/1.03
% 0.68/1.04 joined goal: 1 multiply(a,b) ?= multiply(b,a) to multiply(b,a)
% 0.68/1.04 goal joined
% 0.68/1.04 % SZS status Unsatisfiable
% 0.68/1.04 #START OF PROOF
% 0.68/1.04 % SZS output start CNFRefutation
% 0.68/1.04 cnf('0.1.0.0',axiom,
% 0.68/1.04 ( X1 = double_divide(inverse(double_divide(X2,inverse(double_divide(inverse(X1),double_divide(X2,X3))))),X3) ),
% 0.68/1.04 file('/tmp/WALDMEISTER_31901_n006')).
% 0.68/1.04 cnf('0.1.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(inverse(double_divide(X2,inverse(double_divide(inverse(X1),double_divide(X2,X3))))),X3) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.68/1.04 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.1.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),X3) = X2 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_1]).
% 0.68/1.04 cnf('0.2.0.0',axiom,
% 0.68/1.04 ( inverse(double_divide(X1,X2)) = multiply(X2,X1) ),
% 0.68/1.04 file('/tmp/WALDMEISTER_31901_n006')).
% 0.68/1.04 cnf('0.2.1.0',plain,
% 0.68/1.04 ( inverse(double_divide(X1,X2)) = multiply(X2,X1) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.68/1.04 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.68/1.04 cnf('0.2.2.0',plain,
% 0.68/1.04 ( inverse(double_divide(X1,X2)) = multiply(X2,X1) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_2]).
% 0.68/1.04 cnf('0.3.0.0',plain,
% 0.68/1.04 ( double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),X3) = X2 ),
% 0.68/1.04 inference(interreduction_right,[status(thm)],['0.1.2.0'])).
% 0.68/1.04 cnf('0.3.0.1',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(double_divide(inverse(X2),double_divide(X1,X3))),X1),X3) = X2 ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.3.0.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.3.0.2',plain,
% 0.68/1.04 ( double_divide(multiply(multiply(double_divide(X1,X3),inverse(X2)),X1),X3) = X2 ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.3.0.1','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.3.1.0',plain,
% 0.68/1.04 ( double_divide(multiply(multiply(double_divide(X1,X3),inverse(X2)),X1),X3) = X2 ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.3.0.2']),
% 0.68/1.04 [weight('<131,1,2,[0,0,0,0]>')]).
% 0.68/1.04 cnf('0.3.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(multiply(double_divide(X1,X2),inverse(X3)),X1),X2) = X3 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_3]).
% 0.68/1.04 cnf('0.4.0.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(multiply(double_divide(X2,X1),inverse(X3)),X2)) = inverse(X3) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.2.2.0','0.3.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.4.1.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(multiply(double_divide(X2,X1),inverse(X3)),X2)) = inverse(X3) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.68/1.04 [weight('<142,3,2,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.4.2.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(multiply(double_divide(X2,X1),inverse(X3)),X2)) = inverse(X3) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_4]).
% 0.68/1.04 cnf('0.5.0.0',plain,
% 0.68/1.04 ( double_divide(X1,X2) = double_divide(multiply(multiply(double_divide(X3,X4),multiply(X2,X1)),X3),X4) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.3.2.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1.2','L')]).
% 0.68/1.04 cnf('0.5.1.0',plain,
% 0.68/1.04 ( double_divide(X1,X2) = double_divide(multiply(multiply(double_divide(X3,X4),multiply(X2,X1)),X3),X4) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.68/1.04 [weight('<179,3,2,[1,0,0,6]>')]).
% 0.68/1.04 cnf('0.5.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(multiply(double_divide(X1,X2),multiply(X3,X4)),X1),X2) = double_divide(X4,X3) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_5]).
% 0.68/1.04 cnf('0.6.0.0',plain,
% 0.68/1.04 ( inverse(double_divide(X1,X2)) = multiply(X3,multiply(multiply(double_divide(X4,X3),multiply(X2,X1)),X4)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.4.2.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2.1.2','L')]).
% 0.68/1.04 cnf('0.6.0.1',plain,
% 0.68/1.04 ( multiply(X2,X1) = multiply(X3,multiply(multiply(double_divide(X4,X3),multiply(X2,X1)),X4)) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.6.0.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.6.1.0',plain,
% 0.68/1.04 ( multiply(X2,X1) = multiply(X3,multiply(multiply(double_divide(X4,X3),multiply(X2,X1)),X4)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.6.0.1']),
% 0.68/1.04 [weight('<179,4,2,[1,0,0,7]>')]).
% 0.68/1.04 cnf('0.6.2.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(multiply(double_divide(X2,X1),multiply(X3,X4)),X2)) = multiply(X3,X4) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_6]).
% 0.68/1.04 cnf('0.7.0.0',plain,
% 0.68/1.04 ( double_divide(X1,multiply(double_divide(X1,double_divide(X2,X3)),inverse(X4))) = double_divide(multiply(inverse(X4),X2),X3) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.5.2.0','0.4.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.7.1.0',plain,
% 0.68/1.04 ( double_divide(X1,multiply(double_divide(X1,double_divide(X2,X3)),inverse(X4))) = double_divide(multiply(inverse(X4),X2),X3) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.68/1.04 [weight('<186,5,4,[1,0,0,2]>')]).
% 0.68/1.04 cnf('0.7.2.0',plain,
% 0.68/1.04 ( double_divide(X1,multiply(double_divide(X1,double_divide(X2,X3)),inverse(X4))) = double_divide(multiply(inverse(X4),X2),X3) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_7]).
% 0.68/1.04 cnf('0.8.0.0',plain,
% 0.68/1.04 ( multiply(multiply(double_divide(X1,double_divide(X2,X3)),inverse(X4)),X1) = multiply(X3,multiply(inverse(X4),X2)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.6.2.0','0.4.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2.1','L')]).
% 0.68/1.04 cnf('0.8.1.0',plain,
% 0.68/1.04 ( multiply(multiply(double_divide(X1,double_divide(X2,X3)),inverse(X4)),X1) = multiply(X3,multiply(inverse(X4),X2)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.68/1.04 [weight('<186,6,4,[1,0,0,3]>')]).
% 0.68/1.04 cnf('0.8.2.0',plain,
% 0.68/1.04 ( multiply(multiply(double_divide(X1,double_divide(X2,X3)),inverse(X4)),X1) = multiply(X3,multiply(inverse(X4),X2)) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_8]).
% 0.68/1.04 cnf('0.9.0.0',plain,
% 0.68/1.04 ( X1 = double_divide(multiply(X2,multiply(inverse(X1),X3)),double_divide(X3,X2)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.3.2.0','0.8.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.9.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(multiply(X2,multiply(inverse(X1),X3)),double_divide(X3,X2)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.68/1.04 [weight('<131,8,3,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.9.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(X1,multiply(inverse(X2),X3)),double_divide(X3,X1)) = X2 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_9]).
% 0.68/1.04 cnf('0.10.0.0',plain,
% 0.68/1.04 ( inverse(X1) = multiply(double_divide(X2,X3),multiply(X3,multiply(inverse(X1),X2))) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.4.2.0','0.8.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.10.1.0',plain,
% 0.68/1.04 ( inverse(X1) = multiply(double_divide(X2,X3),multiply(X3,multiply(inverse(X1),X2))) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.68/1.04 [weight('<142,8,4,[0,0,0,2]>')]).
% 0.68/1.04 cnf('0.10.2.0',plain,
% 0.68/1.04 ( multiply(double_divide(X1,X2),multiply(X2,multiply(inverse(X3),X1))) = inverse(X3) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_10]).
% 0.68/1.04 cnf('0.12.0.0',plain,
% 0.68/1.04 ( inverse(double_divide(X1,X2)) = multiply(double_divide(X3,X4),multiply(X4,multiply(multiply(X2,X1),X3))) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.10.2.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2.2.1','L')]).
% 0.68/1.04 cnf('0.12.0.1',plain,
% 0.68/1.04 ( multiply(X2,X1) = multiply(double_divide(X3,X4),multiply(X4,multiply(multiply(X2,X1),X3))) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.12.0.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.12.1.0',plain,
% 0.68/1.04 ( multiply(X2,X1) = multiply(double_divide(X3,X4),multiply(X4,multiply(multiply(X2,X1),X3))) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.12.0.1']),
% 0.68/1.04 [weight('<179,10,2,[1,0,0,7]>')]).
% 0.68/1.04 cnf('0.12.2.0',plain,
% 0.68/1.04 ( multiply(double_divide(X1,X2),multiply(X2,multiply(multiply(X3,X4),X1))) = multiply(X3,X4) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_12]).
% 0.68/1.04 cnf('0.15.0.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(inverse(X2),X3)) = multiply(multiply(X4,inverse(X2)),multiply(multiply(double_divide(X5,double_divide(X3,X1)),inverse(X4)),X5)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.8.2.0','0.3.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.15.0.1',plain,
% 0.68/1.04 ( multiply(X1,multiply(inverse(X2),X3)) = multiply(multiply(X4,inverse(X2)),multiply(X1,multiply(inverse(X4),X3))) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.15.0.0','0.8.2.0',theory(equality)]),
% 0.68/1.04 [pos('R.2','L')]).
% 0.68/1.04 cnf('0.15.1.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(inverse(X2),X3)) = multiply(multiply(X4,inverse(X2)),multiply(X1,multiply(inverse(X4),X3))) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.15.0.1']),
% 0.68/1.04 [weight('<215,8,3,[1,0,0,2]>')]).
% 0.68/1.04 cnf('0.15.2.0',plain,
% 0.68/1.04 ( multiply(multiply(X1,inverse(X2)),multiply(X3,multiply(inverse(X1),X4))) = multiply(X3,multiply(inverse(X2),X4)) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_15]).
% 0.68/1.04 cnf('0.16.0.0',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X1),X2),X3) = double_divide(multiply(X3,multiply(inverse(X4),X2)),multiply(X4,inverse(X1))) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.7.2.0','0.9.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2.1','L')]).
% 0.68/1.04 cnf('0.16.1.0',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X1),X2),X3) = double_divide(multiply(X3,multiply(inverse(X4),X2)),multiply(X4,inverse(X1))) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.68/1.04 [weight('<215,9,7,[0,0,0,3]>')]).
% 0.68/1.04 cnf('0.16.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(X1,multiply(inverse(X2),X3)),multiply(X2,inverse(X4))) = double_divide(multiply(inverse(X4),X3),X1) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_16]).
% 0.68/1.04 cnf('0.21.0.0',plain,
% 0.68/1.04 ( X1 = double_divide(multiply(X2,X3),double_divide(multiply(multiply(X2,X3),X4),double_divide(X4,inverse(X1)))) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.9.2.0','0.12.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.21.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(multiply(X2,X3),double_divide(multiply(multiply(X2,X3),X4),double_divide(X4,inverse(X1)))) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.68/1.04 [weight('<239,12,9,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.21.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(X1,X2),double_divide(multiply(multiply(X1,X2),X3),double_divide(X3,inverse(X4)))) = X4 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_21]).
% 0.68/1.04 cnf('0.22.0.0',plain,
% 0.68/1.04 ( X1 = double_divide(multiply(double_divide(X2,double_divide(X2,inverse(X1))),inverse(X3)),X3) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.21.2.0','0.3.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.22.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(multiply(double_divide(X2,double_divide(X2,inverse(X1))),inverse(X3)),X3) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.68/1.04 [weight('<155,21,3,[1,0,0,4]>')]).
% 0.68/1.04 cnf('0.22.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(double_divide(X1,double_divide(X1,inverse(X2))),inverse(X3)),X3) = X2 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_22]).
% 0.68/1.04 cnf('0.23.0.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(double_divide(X2,double_divide(X2,inverse(X3))),inverse(X1))) = inverse(X3) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.2.2.0','0.22.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.23.1.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(double_divide(X2,double_divide(X2,inverse(X3))),inverse(X1))) = inverse(X3) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.68/1.04 [weight('<167,22,2,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.23.2.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(double_divide(X2,double_divide(X2,inverse(X3))),inverse(X1))) = inverse(X3) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_23]).
% 0.68/1.04 cnf('0.24.0.0',plain,
% 0.68/1.04 ( double_divide(inverse(double_divide(X1,X2)),double_divide(X3,double_divide(X3,inverse(X4)))) = double_divide(multiply(inverse(X4),X1),X2) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.5.2.0','0.23.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.24.0.1',plain,
% 0.68/1.04 ( double_divide(multiply(X2,X1),double_divide(X3,double_divide(X3,inverse(X4)))) = double_divide(multiply(inverse(X4),X1),X2) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.24.0.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.24.1.0',plain,
% 0.68/1.04 ( double_divide(multiply(X2,X1),double_divide(X3,double_divide(X3,inverse(X4)))) = double_divide(multiply(inverse(X4),X1),X2) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.24.0.1']),
% 0.68/1.04 [weight('<186,23,5,[0,0,0,2]>')]).
% 0.68/1.04 cnf('0.24.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(X1,X2),double_divide(X3,double_divide(X3,inverse(X4)))) = double_divide(multiply(inverse(X4),X2),X1) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_24]).
% 0.68/1.04 cnf('0.25.0.0',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X1),inverse(double_divide(X2,double_divide(X2,inverse(X1))))),double_divide(X3,double_divide(X3,inverse(X4)))) = X4 ),
% 0.68/1.04 inference(cp,[status(thm)],['0.24.2.0','0.22.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.25.0.1',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X4),inverse(double_divide(X2,double_divide(X2,inverse(X1))))),inverse(X1)) = X4 ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.25.0.0','0.24.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.25.0.2',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X4),multiply(double_divide(X2,inverse(X1)),X2)),inverse(X1)) = X4 ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.25.0.1','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.2','L')]).
% 0.68/1.04 cnf('0.25.1.0',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X4),multiply(double_divide(X2,inverse(X1)),X2)),inverse(X1)) = X4 ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.25.0.2']),
% 0.68/1.04 [weight('<181,24,22,[1,0,0,0]>')]).
% 0.68/1.04 cnf('0.25.2.0',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X1),multiply(double_divide(X2,inverse(X3)),X2)),inverse(X3)) = X1 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_25]).
% 0.68/1.04 cnf('0.32.0.0',plain,
% 0.68/1.04 ( multiply(inverse(X1),multiply(inverse(X2),multiply(double_divide(X3,inverse(X1)),X3))) = inverse(X2) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.2.2.0','0.25.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.32.1.0',plain,
% 0.68/1.04 ( multiply(inverse(X1),multiply(inverse(X2),multiply(double_divide(X3,inverse(X1)),X3))) = inverse(X2) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.32.0.0']),
% 0.68/1.04 [weight('<194,25,2,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.32.2.0',plain,
% 0.68/1.04 ( multiply(inverse(X1),multiply(inverse(X2),multiply(double_divide(X3,inverse(X1)),X3))) = inverse(X2) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_32]).
% 0.68/1.04 cnf('0.33.0.0',plain,
% 0.68/1.04 ( double_divide(multiply(inverse(X1),multiply(double_divide(X2,inverse(X3)),X2)),inverse(X3)) = double_divide(inverse(X4),multiply(X4,inverse(X1))) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.16.2.0','0.32.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.33.0.1',plain,
% 0.68/1.04 ( X1 = double_divide(inverse(X4),multiply(X4,inverse(X1))) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.33.0.0','0.25.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.33.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(inverse(X4),multiply(X4,inverse(X1))) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.68/1.04 [weight('<71,32,16,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.33.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(X1),multiply(X1,inverse(X2))) = X2 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_33]).
% 0.68/1.04 cnf('0.34.0.0',plain,
% 0.68/1.04 ( multiply(inverse(X1),multiply(inverse(X2),multiply(double_divide(X3,inverse(X1)),X3))) = multiply(multiply(X4,inverse(X2)),inverse(X4)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.15.2.0','0.32.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.34.0.1',plain,
% 0.68/1.04 ( inverse(X2) = multiply(multiply(X4,inverse(X2)),inverse(X4)) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.34.0.0','0.32.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.34.1.0',plain,
% 0.68/1.04 ( inverse(X2) = multiply(multiply(X4,inverse(X2)),inverse(X4)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.34.0.1']),
% 0.68/1.04 [weight('<79,32,15,[0,0,0,5]>')]).
% 0.68/1.04 cnf('0.34.2.0',plain,
% 0.68/1.04 ( multiply(multiply(X1,inverse(X2)),inverse(X1)) = inverse(X2) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_34]).
% 0.68/1.04 cnf('0.35.0.0',plain,
% 0.68/1.04 ( X1 = double_divide(inverse(multiply(X1,inverse(X2))),inverse(X2)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.33.2.0','0.34.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.35.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(inverse(multiply(X1,inverse(X2))),inverse(X2)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.68/1.04 [weight('<89,34,33,[0,0,0,3]>')]).
% 0.68/1.04 cnf('0.35.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(multiply(X1,inverse(X2))),inverse(X2)) = X1 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_35]).
% 0.68/1.04 cnf('0.36.0.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(X2)) = double_divide(inverse(inverse(X2)),inverse(X1)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.35.2.0','0.34.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.36.1.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(X2)) = double_divide(inverse(inverse(X2)),inverse(X1)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.36.0.0']),
% 0.68/1.04 [weight('<76,35,34,[1,0,0,2]>')]).
% 0.68/1.04 cnf('0.36.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(inverse(X1)),inverse(X2)) = multiply(X2,inverse(X1)) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_36]).
% 0.68/1.04 cnf('0.39.0.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(double_divide(X2,X3))) = double_divide(inverse(multiply(X3,X2)),inverse(X1)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.36.2.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.39.0.1',plain,
% 0.68/1.04 ( multiply(X1,multiply(X3,X2)) = double_divide(inverse(multiply(X3,X2)),inverse(X1)) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.39.0.0','0.2.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.39.1.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(X3,X2)) = double_divide(inverse(multiply(X3,X2)),inverse(X1)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.39.0.1']),
% 0.68/1.04 [weight('<103,36,2,[1,0,0,2]>')]).
% 0.68/1.04 cnf('0.39.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(multiply(X1,X2)),inverse(X3)) = multiply(X3,multiply(X1,X2)) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_39]).
% 0.68/1.04 cnf('0.40.0.0',plain,
% 0.68/1.04 ( double_divide(inverse(multiply(X1,inverse(X2))),inverse(X2)) = X1 ),
% 0.68/1.04 inference(interreduction_right,[status(thm)],['0.35.2.0'])).
% 0.68/1.04 cnf('0.40.0.1',plain,
% 0.68/1.04 ( multiply(X2,multiply(X1,inverse(X2))) = X1 ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.40.0.0','0.39.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.40.1.0',plain,
% 0.68/1.04 ( multiply(X2,multiply(X1,inverse(X2))) = X1 ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.40.0.1']),
% 0.68/1.04 [weight('<55,35,39,[0,0,0,0]>')]).
% 0.68/1.04 cnf('0.40.2.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(X2,inverse(X1))) = X2 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_40]).
% 0.68/1.04 cnf('0.41.0.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(X2,multiply(X3,inverse(X2)))) = double_divide(inverse(X3),inverse(X1)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.39.2.0','0.40.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1.1','L')]).
% 0.68/1.04 cnf('0.41.0.1',plain,
% 0.68/1.04 ( multiply(X1,X3) = double_divide(inverse(X3),inverse(X1)) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.41.0.0','0.40.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.41.1.0',plain,
% 0.68/1.04 ( multiply(X1,X3) = double_divide(inverse(X3),inverse(X1)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.41.0.1']),
% 0.68/1.04 [weight('<53,40,39,[0,0,0,2]>')]).
% 0.68/1.04 cnf('0.41.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(X1),inverse(X2)) = multiply(X2,X1) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_41]).
% 0.68/1.04 cnf('0.45.0.0',plain,
% 0.68/1.04 ( multiply(X1,multiply(double_divide(X2,double_divide(X2,inverse(X3))),inverse(X1))) = inverse(X3) ),
% 0.68/1.04 inference(interreduction_right,[status(thm)],['0.23.2.0'])).
% 0.68/1.04 cnf('0.45.0.1',plain,
% 0.68/1.04 ( double_divide(X2,double_divide(X2,inverse(X3))) = inverse(X3) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.45.0.0','0.40.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.45.1.0',plain,
% 0.68/1.04 ( double_divide(X2,double_divide(X2,inverse(X3))) = inverse(X3) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.45.0.1']),
% 0.68/1.04 [weight('<62,23,40,[0,0,0,0]>')]).
% 0.68/1.04 cnf('0.45.2.0',plain,
% 0.68/1.04 ( double_divide(X1,double_divide(X1,inverse(X2))) = inverse(X2) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_45]).
% 0.68/1.04 cnf('0.47.0.0',plain,
% 0.68/1.04 ( inverse(X1) = double_divide(inverse(X2),multiply(X1,X2)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.45.2.0','0.41.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.47.1.0',plain,
% 0.68/1.04 ( inverse(X1) = double_divide(inverse(X2),multiply(X1,X2)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.68/1.04 [weight('<62,45,41,[1,0,0,2]>')]).
% 0.68/1.04 cnf('0.47.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(X1),multiply(X2,X1)) = inverse(X2) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_47]).
% 0.68/1.04 cnf('0.48.0.0',plain,
% 0.68/1.04 ( inverse(inverse(X1)) = X1 ),
% 0.68/1.04 inference(cp,[status(thm)],['0.47.2.0','0.33.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.48.1.0',plain,
% 0.68/1.04 ( inverse(inverse(X1)) = X1 ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.48.0.0']),
% 0.68/1.04 [weight('<19,47,33,[1,0,0,0]>')]).
% 0.68/1.04 cnf('0.48.2.0',plain,
% 0.68/1.04 ( inverse(inverse(X1)) = X1 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 0.68/1.04 [u,rule_48]).
% 0.68/1.04 cnf('0.51.0.0',plain,
% 0.68/1.04 ( inverse(inverse(X1)) = double_divide(X2,double_divide(X2,X1)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.45.2.0','0.48.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2.2','L')]).
% 0.68/1.04 cnf('0.51.0.1',plain,
% 0.68/1.04 ( X1 = double_divide(X2,double_divide(X2,X1)) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.51.0.0','0.48.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.51.1.0',plain,
% 0.68/1.04 ( X1 = double_divide(X2,double_divide(X2,X1)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.51.0.1']),
% 0.68/1.04 [weight('<41,48,45,[0,0,0,4]>')]).
% 0.68/1.04 cnf('0.51.2.0',plain,
% 0.68/1.04 ( double_divide(X1,double_divide(X1,X2)) = X2 ),
% 0.68/1.04 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_51]).
% 0.68/1.04 cnf('0.55.0.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(X2)) = double_divide(X2,inverse(X1)) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.41.2.0','0.48.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.1','L')]).
% 0.68/1.04 cnf('0.55.1.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(X2)) = double_divide(X2,inverse(X1)) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.55.0.0']),
% 0.68/1.04 [weight('<44,48,41,[0,0,0,1]>')]).
% 0.68/1.04 cnf('0.55.2.0',plain,
% 0.68/1.04 ( double_divide(X1,inverse(X2)) = multiply(X2,inverse(X1)) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_55]).
% 0.68/1.04 cnf('0.56.0.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(X2)) = double_divide(inverse(X1),X2) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.51.2.0','0.33.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.56.1.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(X2)) = double_divide(inverse(X1),X2) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.68/1.04 [weight('<44,51,33,[1,0,0,2]>')]).
% 0.68/1.04 cnf('0.56.2.0',plain,
% 0.68/1.04 ( double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)) ),
% 0.68/1.04 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.68/1.04 [x,rule_56]).
% 0.68/1.04 cnf('0.63.0.0',plain,
% 0.68/1.04 ( multiply(X1,inverse(inverse(X2))) = multiply(X2,inverse(inverse(X1))) ),
% 0.68/1.04 inference(cp,[status(thm)],['0.56.2.0','0.55.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('0.63.0.1',plain,
% 0.68/1.04 ( multiply(X1,X2) = multiply(X2,inverse(inverse(X1))) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.63.0.0','0.48.2.0',theory(equality)]),
% 0.68/1.04 [pos('L.2','L')]).
% 0.68/1.04 cnf('0.63.0.2',plain,
% 0.68/1.04 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.68/1.04 inference(reduction,[status(thm)],['0.63.0.1','0.48.2.0',theory(equality)]),
% 0.68/1.04 [pos('R.2','L')]).
% 0.68/1.04 cnf('0.63.1.0',plain,
% 0.68/1.04 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.68/1.04 inference(weigh,[status(thm)],['0.63.0.2']),
% 0.68/1.04 [weight('<48,56,55,[1,0,0,0]>')]).
% 0.68/1.04 cnf('0.63.2.0',plain,
% 0.68/1.04 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.68/1.04 inference(activate,[status(thm)],['0.63.1.0']),
% 0.68/1.04 [equation_3]).
% 0.68/1.04 cnf('1.0.0.0',conjecture,
% 0.68/1.04 ( multiply(a,b) = multiply(b,a) ),
% 0.68/1.04 file('/tmp/WALDMEISTER_31901_n006',conjecture_1)).
% 0.68/1.04 cnf('1.0.0.1',plain,
% 0.68/1.04 ( multiply(b,a) = multiply(b,a) ),
% 0.68/1.04 inference(reduction,[status(thm)],['1.0.0.0','0.63.2.0',theory(equality)]),
% 0.68/1.04 [pos('L','L')]).
% 0.68/1.04 cnf('1.0.0.2',plain,
% 0.68/1.04 ( $true ),
% 0.68/1.04 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.68/1.04 [conjecture_1]).
% 0.68/1.04
% 0.68/1.04 Proved Goals:
% 0.68/1.04 No. 1: multiply(a,b) ?= multiply(b,a) joined, current: multiply(b,a) = multiply(b,a)
% 0.68/1.04 1 goal was specified, which was proved.
% 0.68/1.04 % SZS output end CNFRefutation
% 0.68/1.04 #END OF PROOF
% 0.68/1.04
% 0.68/1.04 Problem WALDMEISTER_31901_n006
% 0.68/1.04 CPs.gen 2021
% 0.68/1.04 CPs.reexp 0
% 0.68/1.04 Select 102
% 0.68/1.04 R 60
% 0.68/1.04 E 3
% 0.68/1.04 vsize 6.4M
% 0.68/1.04 rss 3.8M
% 0.68/1.04 process.time 0.012s
% 0.68/1.04 wallclock.time 0.012s
% 0.68/1.04 status S
% 0.68/1.04
% 0.68/1.04
% 0.68/1.04 Waldmeister states: Goal proved.
% 0.68/1.04 % SZS status Unsatisfiable
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