TSTP Solution File: GRP600-1 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP600-1 : 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 12:27:04 EDT 2022
% Result : Unsatisfiable 0.59s 1.00s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP600-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n006.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 10:48:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.99 * |/ | \/ | *
% 0.59/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.99 * A. Jaeger and B. Loechner | | *
% 0.59/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Goals:
% 0.59/0.99 ------
% 0.59/0.99
% 0.59/0.99 ( 1) multiply(a,b) ?=? multiply(b,a)
% 0.59/0.99
% 0.59/0.99 Detected structure: Orkus
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/1.00 joined goal: 1 multiply(a,b) ?= multiply(b,a) to multiply(b,a)
% 0.59/1.00 goal joined
% 0.59/1.00 % SZS status Unsatisfiable
% 0.59/1.00 #START OF PROOF
% 0.59/1.00 % SZS output start CNFRefutation
% 0.59/1.00 cnf('0.1.0.0',axiom,
% 0.59/1.00 ( X1 = double_divide(double_divide(X2,X3),inverse(double_divide(X2,inverse(double_divide(inverse(X1),X3))))) ),
% 0.59/1.00 file('/tmp/WALDMEISTER_6736_n006')).
% 0.59/1.00 cnf('0.1.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X2,X3),inverse(double_divide(X2,inverse(double_divide(inverse(X1),X3))))) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.59/1.00 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.1.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(inverse(X3),X2))))) = X3 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_1]).
% 0.59/1.00 cnf('0.2.0.0',axiom,
% 0.59/1.00 ( inverse(double_divide(X1,X2)) = multiply(X2,X1) ),
% 0.59/1.00 file('/tmp/WALDMEISTER_6736_n006')).
% 0.59/1.00 cnf('0.2.1.0',plain,
% 0.59/1.00 ( inverse(double_divide(X1,X2)) = multiply(X2,X1) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.59/1.00 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.59/1.00 cnf('0.2.2.0',plain,
% 0.59/1.00 ( inverse(double_divide(X1,X2)) = multiply(X2,X1) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_2]).
% 0.59/1.00 cnf('0.3.0.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(inverse(X3),X2))))) = X3 ),
% 0.59/1.00 inference(interreduction_right,[status(thm)],['0.1.2.0'])).
% 0.59/1.00 cnf('0.3.0.1',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),multiply(inverse(double_divide(inverse(X3),X2)),X1)) = X3 ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.3.0.0','0.2.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.3.0.2',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(X3)),X1)) = X3 ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.3.0.1','0.2.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2.1','L')]).
% 0.59/1.00 cnf('0.3.1.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(X3)),X1)) = X3 ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.3.0.2']),
% 0.59/1.00 [weight('<131,1,2,[0,0,0,0]>')]).
% 0.59/1.00 cnf('0.3.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(X3)),X1)) = X3 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_3]).
% 0.59/1.00 cnf('0.4.0.0',plain,
% 0.59/1.00 ( multiply(multiply(multiply(X1,inverse(X2)),X3),double_divide(X3,X1)) = inverse(X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.2.2.0','0.3.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.4.1.0',plain,
% 0.59/1.00 ( multiply(multiply(multiply(X1,inverse(X2)),X3),double_divide(X3,X1)) = inverse(X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.59/1.00 [weight('<142,3,2,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.4.2.0',plain,
% 0.59/1.00 ( multiply(multiply(multiply(X1,inverse(X2)),X3),double_divide(X3,X1)) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_4]).
% 0.59/1.00 cnf('0.7.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,inverse(X3))),inverse(X3)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.3.2.0','0.4.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.7.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,inverse(X3))),inverse(X3)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.59/1.00 [weight('<181,4,3,[0,0,0,4]>')]).
% 0.59/1.00 cnf('0.7.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(double_divide(inverse(X1),X2),multiply(X2,inverse(X3))),inverse(X3)) = X1 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_7]).
% 0.59/1.00 cnf('0.8.0.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(inverse(X2),double_divide(double_divide(inverse(X1),X3),multiply(X3,inverse(X2)))) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.4.2.0','0.4.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.8.1.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(inverse(X2),double_divide(double_divide(inverse(X1),X3),multiply(X3,inverse(X2)))) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.59/1.00 [weight('<194,4,4,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.8.2.0',plain,
% 0.59/1.00 ( multiply(inverse(X1),double_divide(double_divide(inverse(X2),X3),multiply(X3,inverse(X1)))) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_8]).
% 0.59/1.00 cnf('0.13.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(X2,multiply(multiply(multiply(multiply(X3,inverse(X2)),X4),inverse(X1)),double_divide(X4,X3))) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.3.2.0','0.3.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.13.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(X2,multiply(multiply(multiply(multiply(X3,inverse(X2)),X4),inverse(X1)),double_divide(X4,X3))) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.59/1.00 [weight('<271,3,3,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.13.2.0',plain,
% 0.59/1.00 ( double_divide(X1,multiply(multiply(multiply(multiply(X2,inverse(X1)),X3),inverse(X4)),double_divide(X3,X2))) = X4 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_13]).
% 0.59/1.00 cnf('0.14.0.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(multiply(multiply(multiply(multiply(X2,inverse(X3)),X4),inverse(X1)),double_divide(X4,X2)),X3) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.4.2.0','0.3.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.14.1.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(multiply(multiply(multiply(multiply(X2,inverse(X3)),X4),inverse(X1)),double_divide(X4,X2)),X3) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.59/1.00 [weight('<287,4,3,[1,0,0,7]>')]).
% 0.59/1.00 cnf('0.14.2.0',plain,
% 0.59/1.00 ( multiply(multiply(multiply(multiply(multiply(X1,inverse(X2)),X3),inverse(X4)),double_divide(X3,X1)),X2) = inverse(X4) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_14]).
% 0.59/1.00 cnf('0.15.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(X2,multiply(inverse(X2),double_divide(double_divide(X3,X4),multiply(multiply(X4,inverse(inverse(X1))),X3)))) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.13.2.0','0.14.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2.1','L')]).
% 0.59/1.00 cnf('0.15.0.1',plain,
% 0.59/1.00 ( X1 = double_divide(X2,multiply(inverse(X2),inverse(X1))) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.15.0.0','0.3.2.0',theory(equality)]),
% 0.59/1.00 [pos('R.2.2','L')]).
% 0.59/1.00 cnf('0.15.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(X2,multiply(inverse(X2),inverse(X1))) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.15.0.1']),
% 0.59/1.00 [weight('<71,14,13,[0,0,0,3]>')]).
% 0.59/1.00 cnf('0.15.2.0',plain,
% 0.59/1.00 ( double_divide(X1,multiply(inverse(X1),inverse(X2))) = X2 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_15]).
% 0.59/1.00 cnf('0.16.0.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(multiply(inverse(X2),double_divide(double_divide(X3,X4),multiply(multiply(X4,inverse(inverse(X1))),X3))),X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.14.2.0','0.14.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1.1','L')]).
% 0.59/1.00 cnf('0.16.0.1',plain,
% 0.59/1.00 ( inverse(X1) = multiply(multiply(inverse(X2),inverse(X1)),X2) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.16.0.0','0.3.2.0',theory(equality)]),
% 0.59/1.00 [pos('R.1.2','L')]).
% 0.59/1.00 cnf('0.16.1.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(multiply(inverse(X2),inverse(X1)),X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.16.0.1']),
% 0.59/1.00 [weight('<79,14,14,[0,0,0,2]>')]).
% 0.59/1.00 cnf('0.16.2.0',plain,
% 0.59/1.00 ( multiply(multiply(inverse(X1),inverse(X2)),X1) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_16]).
% 0.59/1.00 cnf('0.17.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X2,inverse(X2)),inverse(X1)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.3.2.0','0.16.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.17.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X2,inverse(X2)),inverse(X1)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.59/1.00 [weight('<71,16,3,[0,0,0,4]>')]).
% 0.59/1.00 cnf('0.17.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = X2 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_17]).
% 0.59/1.00 cnf('0.21.0.0',plain,
% 0.59/1.00 ( double_divide(X1,X2) = double_divide(double_divide(X3,inverse(X3)),multiply(X2,X1)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.17.2.0','0.2.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.21.1.0',plain,
% 0.59/1.00 ( double_divide(X1,X2) = double_divide(double_divide(X3,inverse(X3)),multiply(X2,X1)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.59/1.00 [weight('<107,17,2,[1,0,0,5]>')]).
% 0.59/1.00 cnf('0.21.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,inverse(X1)),multiply(X2,X3)) = double_divide(X3,X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_21]).
% 0.59/1.00 cnf('0.22.0.0',plain,
% 0.59/1.00 ( double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))) = X1 ),
% 0.59/1.00 inference(cp,[status(thm)],['0.21.2.0','0.15.2.0',theory(equality)]),
% 0.59/1.00 [pos('L','L')]).
% 0.59/1.00 cnf('0.22.0.1',plain,
% 0.59/1.00 ( double_divide(inverse(X1),multiply(inverse(X2),X2)) = X1 ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.22.0.0','0.2.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.22.1.0',plain,
% 0.59/1.00 ( double_divide(inverse(X1),multiply(inverse(X2),X2)) = X1 ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.22.0.1']),
% 0.59/1.00 [weight('<71,21,15,[1,0,0,0]>')]).
% 0.59/1.00 cnf('0.22.2.0',plain,
% 0.59/1.00 ( double_divide(inverse(X1),multiply(inverse(X2),X2)) = X1 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_22]).
% 0.59/1.00 cnf('0.23.0.0',plain,
% 0.59/1.00 ( multiply(multiply(inverse(X1),X1),inverse(X2)) = inverse(X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.2.2.0','0.22.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.23.1.0',plain,
% 0.59/1.00 ( multiply(multiply(inverse(X1),X1),inverse(X2)) = inverse(X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.59/1.00 [weight('<79,22,2,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.23.2.0',plain,
% 0.59/1.00 ( multiply(multiply(inverse(X1),X1),inverse(X2)) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_23]).
% 0.59/1.00 cnf('0.24.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(double_divide(inverse(X1),multiply(inverse(X2),X2)),inverse(X3)),inverse(X3)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.7.2.0','0.23.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1.2','L')]).
% 0.59/1.00 cnf('0.24.0.1',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X1,inverse(X3)),inverse(X3)) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.24.0.0','0.22.2.0',theory(equality)]),
% 0.59/1.00 [pos('R.1.1','L')]).
% 0.59/1.00 cnf('0.24.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X1,inverse(X3)),inverse(X3)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.24.0.1']),
% 0.59/1.00 [weight('<71,23,7,[0,0,0,6]>')]).
% 0.59/1.00 cnf('0.24.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,inverse(X2)),inverse(X2)) = X1 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_24]).
% 0.59/1.00 cnf('0.25.0.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(inverse(X2),double_divide(double_divide(inverse(X1),multiply(inverse(X3),X3)),inverse(X2))) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.8.2.0','0.23.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2.2','L')]).
% 0.59/1.00 cnf('0.25.0.1',plain,
% 0.59/1.00 ( inverse(X1) = multiply(inverse(X2),double_divide(X1,inverse(X2))) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.25.0.0','0.22.2.0',theory(equality)]),
% 0.59/1.00 [pos('R.2.1','L')]).
% 0.59/1.00 cnf('0.25.1.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(inverse(X2),double_divide(X1,inverse(X2))) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.25.0.1']),
% 0.59/1.00 [weight('<79,23,8,[0,0,0,8]>')]).
% 0.59/1.00 cnf('0.25.2.0',plain,
% 0.59/1.00 ( multiply(inverse(X1),double_divide(X2,inverse(X1))) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_25]).
% 0.59/1.00 cnf('0.31.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(inverse(X2),inverse(inverse(X1))),inverse(X2)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.7.2.0','0.21.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.31.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(inverse(X2),inverse(inverse(X1))),inverse(X2)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.59/1.00 [weight('<109,21,7,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.31.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(inverse(X1),inverse(inverse(X2))),inverse(X1)) = X2 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_29]).
% 0.59/1.00 cnf('0.32.0.0',plain,
% 0.59/1.00 ( X1 = inverse(inverse(X1)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.31.2.0','0.24.2.0',theory(equality)]),
% 0.59/1.00 [pos('L','L')]).
% 0.59/1.00 cnf('0.32.1.0',plain,
% 0.59/1.00 ( X1 = inverse(inverse(X1)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.32.0.0']),
% 0.59/1.00 [weight('<19,31,24,[1,0,0,0]>')]).
% 0.59/1.00 cnf('0.32.2.0',plain,
% 0.59/1.00 ( inverse(inverse(X1)) = X1 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_30]).
% 0.59/1.00 cnf('0.34.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X1,X2),inverse(inverse(X2))) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.24.2.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1.2','L')]).
% 0.59/1.00 cnf('0.34.0.1',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X1,X2),X2) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.34.0.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('R.2','L')]).
% 0.59/1.00 cnf('0.34.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(double_divide(X1,X2),X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.34.0.1']),
% 0.59/1.00 [weight('<41,32,24,[0,0,0,3]>')]).
% 0.59/1.00 cnf('0.34.2.0',plain,
% 0.59/1.00 ( double_divide(double_divide(X1,X2),X2) = X1 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_32]).
% 0.59/1.00 cnf('0.35.0.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(X2,double_divide(X1,inverse(inverse(X2)))) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.25.2.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.35.0.1',plain,
% 0.59/1.00 ( inverse(X1) = multiply(X2,double_divide(X1,X2)) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.35.0.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('R.2.2','L')]).
% 0.59/1.00 cnf('0.35.1.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(X2,double_divide(X1,X2)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.35.0.1']),
% 0.59/1.00 [weight('<47,32,25,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.35.2.0',plain,
% 0.59/1.00 ( multiply(X1,double_divide(X2,X1)) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_33]).
% 0.59/1.00 cnf('0.36.0.0',plain,
% 0.59/1.00 ( inverse(inverse(X1)) = multiply(multiply(inverse(X2),X1),X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.16.2.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1.2','L')]).
% 0.59/1.00 cnf('0.36.0.1',plain,
% 0.59/1.00 ( X1 = multiply(multiply(inverse(X2),X1),X2) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.36.0.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('L','L')]).
% 0.59/1.00 cnf('0.36.1.0',plain,
% 0.59/1.00 ( X1 = multiply(multiply(inverse(X2),X1),X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.36.0.1']),
% 0.59/1.00 [weight('<55,32,16,[0,0,0,4]>')]).
% 0.59/1.00 cnf('0.36.2.0',plain,
% 0.59/1.00 ( multiply(multiply(inverse(X1),X2),X1) = X2 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_34]).
% 0.59/1.00 cnf('0.37.0.0',plain,
% 0.59/1.00 ( double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.36.2.0','0.35.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.37.1.0',plain,
% 0.59/1.00 ( double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.37.0.0']),
% 0.59/1.00 [weight('<44,36,35,[1,0,0,1]>')]).
% 0.59/1.00 cnf('0.37.2.0',plain,
% 0.59/1.00 ( double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_35]).
% 0.59/1.00 cnf('0.38.0.0',plain,
% 0.59/1.00 ( multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.37.2.0','0.32.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.38.1.0',plain,
% 0.59/1.00 ( multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.59/1.00 [weight('<53,37,32,[1,0,0,2]>')]).
% 0.59/1.00 cnf('0.38.2.0',plain,
% 0.59/1.00 ( multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_36]).
% 0.59/1.00 cnf('0.39.0.0',plain,
% 0.59/1.00 ( double_divide(X1,multiply(inverse(X1),inverse(X2))) = X2 ),
% 0.59/1.00 inference(interreduction_right,[status(thm)],['0.15.2.0'])).
% 0.59/1.00 cnf('0.39.0.1',plain,
% 0.59/1.00 ( double_divide(X1,double_divide(X1,X2)) = X2 ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.39.0.0','0.38.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.2','L')]).
% 0.59/1.00 cnf('0.39.1.0',plain,
% 0.59/1.00 ( double_divide(X1,double_divide(X1,X2)) = X2 ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.39.0.1']),
% 0.59/1.00 [weight('<41,15,38,[0,0,0,0]>')]).
% 0.59/1.00 cnf('0.39.2.0',plain,
% 0.59/1.00 ( double_divide(X1,double_divide(X1,X2)) = X2 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.59/1.00 [u,rule_37]).
% 0.59/1.00 cnf('0.40.0.0',plain,
% 0.59/1.00 ( X1 = double_divide(X2,double_divide(X1,X2)) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.34.2.0','0.39.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.40.1.0',plain,
% 0.59/1.00 ( X1 = double_divide(X2,double_divide(X1,X2)) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.59/1.00 [weight('<41,39,34,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.40.2.0',plain,
% 0.59/1.00 ( double_divide(X1,double_divide(X2,X1)) = X2 ),
% 0.59/1.00 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_38]).
% 0.59/1.00 cnf('0.43.0.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(double_divide(X2,X1),X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.36.2.0','0.38.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.43.1.0',plain,
% 0.59/1.00 ( inverse(X1) = multiply(double_divide(X2,X1),X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.43.0.0']),
% 0.59/1.00 [weight('<47,38,36,[0,0,0,1]>')]).
% 0.59/1.00 cnf('0.43.2.0',plain,
% 0.59/1.00 ( multiply(double_divide(X1,X2),X1) = inverse(X2) ),
% 0.59/1.00 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 0.59/1.00 [x,rule_41]).
% 0.59/1.00 cnf('0.47.0.0',plain,
% 0.59/1.00 ( inverse(double_divide(X1,X2)) = multiply(X1,X2) ),
% 0.59/1.00 inference(cp,[status(thm)],['0.43.2.0','0.40.2.0',theory(equality)]),
% 0.59/1.00 [pos('L.1','L')]).
% 0.59/1.00 cnf('0.47.0.1',plain,
% 0.59/1.00 ( multiply(X2,X1) = multiply(X1,X2) ),
% 0.59/1.00 inference(reduction,[status(thm)],['0.47.0.0','0.2.2.0',theory(equality)]),
% 0.59/1.00 [pos('L','L')]).
% 0.59/1.00 cnf('0.47.1.0',plain,
% 0.59/1.00 ( multiply(X2,X1) = multiply(X1,X2) ),
% 0.59/1.00 inference(weigh,[status(thm)],['0.47.0.1']),
% 0.59/1.00 [weight('<48,43,40,[1,0,0,1]>')]).
% 0.59/1.00 cnf('0.47.2.0',plain,
% 0.59/1.00 ( multiply(X1,X2) = multiply(X2,X1) ),
% 0.59/1.00 inference(activate,[status(thm)],['0.47.1.0']),
% 0.59/1.00 [equation_4]).
% 0.59/1.00 cnf('1.0.0.0',conjecture,
% 0.59/1.00 ( multiply(a,b) = multiply(b,a) ),
% 0.59/1.00 file('/tmp/WALDMEISTER_6736_n006',conjecture_1)).
% 0.59/1.00 cnf('1.0.0.1',plain,
% 0.59/1.00 ( multiply(b,a) = multiply(b,a) ),
% 0.59/1.00 inference(reduction,[status(thm)],['1.0.0.0','0.47.2.0',theory(equality)]),
% 0.59/1.00 [pos('L','L')]).
% 0.59/1.00 cnf('1.0.0.2',plain,
% 0.59/1.00 ( $true ),
% 0.59/1.00 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.59/1.00 [conjecture_1]).
% 0.59/1.00
% 0.59/1.00 Proved Goals:
% 0.59/1.00 No. 1: multiply(a,b) ?= multiply(b,a) joined, current: multiply(b,a) = multiply(b,a)
% 0.59/1.00 1 goal was specified, which was proved.
% 0.59/1.00 % SZS output end CNFRefutation
% 0.59/1.00 #END OF PROOF
% 0.59/1.00
% 0.59/1.00 Problem WALDMEISTER_6736_n006
% 0.59/1.00 CPs.gen 985
% 0.59/1.00 CPs.reexp 0
% 0.59/1.00 Select 95
% 0.59/1.00 R 43
% 0.59/1.00 E 4
% 0.59/1.00 vsize 6.4M
% 0.59/1.00 rss 3.8M
% 0.59/1.00 process.time 0.007s
% 0.59/1.00 wallclock.time 0.007s
% 0.59/1.00 status S
% 0.59/1.00
% 0.59/1.00
% 0.59/1.00 Waldmeister states: Goal proved.
% 0.59/1.00 % SZS status Unsatisfiable
%------------------------------------------------------------------------------