TSTP Solution File: LCL096-10 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n020.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 : Sun Jul 17 16:03:29 EDT 2022
% Result : Unsatisfiable 1.07s 1.49s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n020.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 Jul 4 05:11:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.99 ********************************************************************************
% 0.57/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.99 * |/ | \/ | *
% 0.57/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.99 * A. Jaeger and B. Loechner | | *
% 0.57/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.99 ********************************************************************************
% 0.57/0.99
% 0.57/0.99
% 0.57/0.99 Goals:
% 0.57/0.99 ------
% 0.57/0.99
% 0.57/0.99 ( 1) true ?=? is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c))
% 0.57/0.99
% 0.57/0.99 Detected structure: Orkus
% 0.57/0.99 ********************************************************************************
% 0.57/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.99 ********************************************************************************
% 0.57/0.99
% 1.07/1.49 joined goal: 1 true ?= is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) to true
% 1.07/1.49 goal joined
% 1.07/1.49 % SZS status Unsatisfiable
% 1.07/1.49 #START OF PROOF
% 1.07/1.49 % SZS output start CNFRefutation
% 1.07/1.49 cnf('0.1.0.0',axiom,
% 1.07/1.49 ( X1 = ifeq(X2,X2,X1,X3) ),
% 1.07/1.49 file('/tmp/WALDMEISTER_4412_n020')).
% 1.07/1.49 cnf('0.1.1.0',plain,
% 1.07/1.49 ( X1 = ifeq(X2,X2,X1,X3) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.07/1.49 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.1.2.0',plain,
% 1.07/1.49 ( ifeq(X1,X1,X2,X3) = X2 ),
% 1.07/1.49 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_1]).
% 1.07/1.49 cnf('0.2.0.0',axiom,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))) ),
% 1.07/1.49 file('/tmp/WALDMEISTER_4412_n020')).
% 1.07/1.49 cnf('0.2.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.07/1.49 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.07/1.49 cnf('0.2.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_2]).
% 1.07/1.49 cnf('0.3.0.0',axiom,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4)) ),
% 1.07/1.49 file('/tmp/WALDMEISTER_4412_n020')).
% 1.07/1.49 cnf('0.3.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.07/1.49 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.07/1.49 cnf('0.3.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_3]).
% 1.07/1.49 cnf('0.4.0.0',axiom,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4)),X5),X5)) ),
% 1.07/1.49 file('/tmp/WALDMEISTER_4412_n020')).
% 1.07/1.49 cnf('0.4.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4)),X5),X5)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.07/1.49 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.07/1.49 cnf('0.4.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4)),X5),X5)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_4]).
% 1.07/1.49 cnf('0.5.0.0',axiom,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 1.07/1.49 file('/tmp/WALDMEISTER_4412_n020')).
% 1.07/1.49 cnf('0.5.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.07/1.49 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.07/1.49 cnf('0.5.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_5]).
% 1.07/1.49 cnf('0.6.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4)),true,is_a_theorem(X4),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.6.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4)),true,is_a_theorem(X4),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.6.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.6.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4)),true,is_a_theorem(X4),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.6.0.1']),
% 1.07/1.49 [weight('<419,5,3,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.6.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4)),true,is_a_theorem(X4),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_6]).
% 1.07/1.49 cnf('0.7.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.7.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.7.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.7.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.7.0.1']),
% 1.07/1.49 [weight('<305,6,2,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.7.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_7]).
% 1.07/1.49 cnf('0.8.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(equivalent(X4,X2),equivalent(X4,X3))),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.7.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.8.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(equivalent(X4,X2),equivalent(X4,X3))),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.8.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.8.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(equivalent(X4,X2),equivalent(X4,X3))),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.8.0.1']),
% 1.07/1.49 [weight('<419,7,5,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.8.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(equivalent(X4,X2),equivalent(X4,X3))),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_8]).
% 1.07/1.49 cnf('0.10.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X3)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.8.2.0','0.7.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.10.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X3)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.10.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.10.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X3)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.10.0.1']),
% 1.07/1.49 [weight('<181,8,7,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.10.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X3)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_10]).
% 1.07/1.49 cnf('0.11.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.6.2.0','0.10.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.11.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.11.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.11.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.11.0.1']),
% 1.07/1.49 [weight('<181,10,6,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.11.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_11]).
% 1.07/1.49 cnf('0.14.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.11.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.14.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.14.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.14.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.14.0.1']),
% 1.07/1.49 [weight('<271,11,5,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.14.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_14]).
% 1.07/1.49 cnf('0.15.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.14.2.0','0.2.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.15.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.15.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.15.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.15.0.1']),
% 1.07/1.49 [weight('<89,14,2,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.15.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_15]).
% 1.07/1.49 cnf('0.16.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.14.2.0','0.7.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.16.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.16.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.16.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.16.0.1']),
% 1.07/1.49 [weight('<89,14,7,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.16.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_16]).
% 1.07/1.49 cnf('0.17.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(X1,X1)),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.14.2.0','0.16.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.17.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(X1,X1)) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.17.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.17.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(X1,X1)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.17.0.1']),
% 1.07/1.49 [weight('<29,16,14,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.17.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(X1,X1)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_17]).
% 1.07/1.49 cnf('0.21.0.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.17.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.3.1','L')]).
% 1.07/1.49 cnf('0.21.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.21.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R.3','L')]).
% 1.07/1.49 cnf('0.21.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.21.0.1']),
% 1.07/1.49 [weight('<155,17,5,[0,0,0,7]>')]).
% 1.07/1.49 cnf('0.21.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_21]).
% 1.07/1.49 cnf('0.27.0.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.15.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.3.1','L')]).
% 1.07/1.49 cnf('0.27.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,is_a_theorem(X3),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.27.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R.3','L')]).
% 1.07/1.49 cnf('0.27.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,is_a_theorem(X3),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.27.0.1']),
% 1.07/1.49 [weight('<271,15,5,[0,0,0,7]>')]).
% 1.07/1.49 cnf('0.27.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,is_a_theorem(X3),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_27]).
% 1.07/1.49 cnf('0.38.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.6.2.0','0.15.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.38.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.38.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.38.0.1']),
% 1.07/1.49 [weight('<305,15,6,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.38.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_38]).
% 1.07/1.49 cnf('0.40.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.21.2.0','0.2.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.40.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.40.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.40.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.40.0.1']),
% 1.07/1.49 [weight('<305,21,2,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.40.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_40]).
% 1.07/1.49 cnf('0.41.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.21.2.0','0.40.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.41.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.41.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.41.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.41.0.1']),
% 1.07/1.49 [weight('<181,40,21,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.41.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_41]).
% 1.07/1.49 cnf('0.45.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.21.2.0','0.4.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.45.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.45.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.45.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.45.0.1']),
% 1.07/1.49 [weight('<305,21,4,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.45.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_45]).
% 1.07/1.49 cnf('0.62.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.8.2.0','0.38.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.62.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.62.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.62.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.62.0.1']),
% 1.07/1.49 [weight('<305,38,8,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.62.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_62]).
% 1.07/1.49 cnf('0.64.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.6.2.0','0.40.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.64.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.64.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.64.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.64.0.1']),
% 1.07/1.49 [weight('<305,40,6,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.64.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_64]).
% 1.07/1.49 cnf('0.65.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X1),X2),X3),equivalent(X2,X3))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.27.2.0','0.64.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.65.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X1),X2),X3),equivalent(X2,X3))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.65.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.65.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X1),X2),X3),equivalent(X2,X3))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.65.0.1']),
% 1.07/1.49 [weight('<181,64,27,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.65.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X1),X2),X3),equivalent(X2,X3))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_65]).
% 1.07/1.49 cnf('0.67.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X3)),true,is_a_theorem(equivalent(X2,X3)),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.65.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.67.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X3)),true,is_a_theorem(equivalent(X2,X3)),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.67.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.67.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X3)),true,is_a_theorem(equivalent(X2,X3)),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.67.0.1']),
% 1.07/1.49 [weight('<271,65,5,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.67.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X3)),true,is_a_theorem(equivalent(X2,X3)),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.67.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_67]).
% 1.07/1.49 cnf('0.69.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X2,X1)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.67.2.0','0.41.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.69.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X2,X1)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.69.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.69.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X2,X1)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.69.0.1']),
% 1.07/1.49 [weight('<181,67,41,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.69.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X2,X1)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_69]).
% 1.07/1.49 cnf('0.126.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(X3,equivalent(equivalent(X3,equivalent(X4,X4)),X2))))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.8.2.0','0.69.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.126.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(X3,equivalent(equivalent(X3,equivalent(X4,X4)),X2))))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.126.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.126.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(X3,equivalent(equivalent(X3,equivalent(X4,X4)),X2))))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.126.0.1']),
% 1.07/1.49 [weight('<305,69,8,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.126.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(X3,equivalent(equivalent(X3,equivalent(X4,X4)),X2))))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.126.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_126]).
% 1.07/1.49 cnf('0.208.0.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4),X5)),true,ifeq(true,true,is_a_theorem(X5),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.3.1','L')]).
% 1.07/1.49 cnf('0.208.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4),X5)),true,is_a_theorem(X5),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.208.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R.3','L')]).
% 1.07/1.49 cnf('0.208.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4),X5)),true,is_a_theorem(X5),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.208.0.1']),
% 1.07/1.49 [weight('<?,5,3,[1,0,0,7]>')]).
% 1.07/1.49 cnf('0.208.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4),X5)),true,is_a_theorem(X5),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.208.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_208]).
% 1.07/1.49 cnf('0.210.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X4,X1),equivalent(X4,X2)),X3))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.208.2.0','0.45.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.210.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X4,X1),equivalent(X4,X2)),X3))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.210.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.210.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X4,X1),equivalent(X4,X2)),X3))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.210.0.1']),
% 1.07/1.49 [weight('<305,208,45,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.210.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(equivalent(X4,X1),equivalent(X4,X2)),X3))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.210.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_210]).
% 1.07/1.49 cnf('0.224.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4)))),true,is_a_theorem(equivalent(X1,equivalent(X3,X4))),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.62.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.224.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4)))),true,is_a_theorem(equivalent(X1,equivalent(X3,X4))),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.224.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.224.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4)))),true,is_a_theorem(equivalent(X1,equivalent(X3,X4))),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.224.0.1']),
% 1.07/1.49 [weight('<419,62,5,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.224.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4)))),true,is_a_theorem(equivalent(X1,equivalent(X3,X4))),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.224.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_224]).
% 1.07/1.49 cnf('0.230.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,equivalent(equivalent(X1,equivalent(X4,X4)),X3)))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.224.2.0','0.126.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.230.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,equivalent(equivalent(X1,equivalent(X4,X4)),X3)))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.230.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.230.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,equivalent(equivalent(X1,equivalent(X4,X4)),X3)))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.230.0.1']),
% 1.07/1.49 [weight('<305,224,126,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.230.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,equivalent(equivalent(X1,equivalent(X4,X4)),X3)))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.230.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_230]).
% 1.07/1.49 cnf('0.239.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X4)),equivalent(equivalent(X3,X2),X4))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.224.2.0','0.210.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.239.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X4)),equivalent(equivalent(X3,X2),X4))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.239.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.239.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X4)),equivalent(equivalent(X3,X2),X4))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.239.0.1']),
% 1.07/1.49 [weight('<305,224,210,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.239.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X4)),equivalent(equivalent(X3,X2),X4))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.239.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_239]).
% 1.07/1.49 cnf('0.241.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.8.2.0','0.239.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.241.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.241.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.241.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.241.0.1']),
% 1.07/1.49 [weight('<181,239,8,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.241.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.241.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_241]).
% 1.07/1.49 cnf('0.253.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.241.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.253.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.253.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.253.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.253.0.1']),
% 1.07/1.49 [weight('<271,241,5,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.253.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.253.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_253]).
% 1.07/1.49 cnf('0.254.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.253.2.0','0.239.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.254.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.254.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.254.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.254.0.1']),
% 1.07/1.49 [weight('<181,253,239,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.254.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.254.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_254]).
% 1.07/1.49 cnf('0.265.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4),equivalent(X3,X4))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.224.2.0','0.230.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.265.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4),equivalent(X3,X4))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.265.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.265.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4),equivalent(X3,X4))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.265.0.1']),
% 1.07/1.49 [weight('<305,230,224,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.265.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4),equivalent(X3,X4))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.265.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_265]).
% 1.07/1.49 cnf('0.383.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X2),X4))),equivalent(X1,X4))),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.8.2.0','0.254.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.383.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X2),X4))),equivalent(X1,X4))) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.383.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.383.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X2),X4))),equivalent(X1,X4))) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.383.0.1']),
% 1.07/1.49 [weight('<305,254,8,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.383.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X2),X4))),equivalent(X1,X4))) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.383.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_383]).
% 1.07/1.49 cnf('0.434.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(equivalent(X3,X2),X4))),X4)),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.6.2.0','0.383.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.434.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(equivalent(X3,X2),X4))),X4)) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.434.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.434.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(equivalent(X3,X2),X4))),X4)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.434.0.1']),
% 1.07/1.49 [weight('<305,383,6,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.434.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(equivalent(X3,X2),X4))),X4)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.434.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_434]).
% 1.07/1.49 cnf('0.446.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X1,equivalent(X3,X2)),X4))),X4)),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.14.2.0','0.434.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.446.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X1,equivalent(X3,X2)),X4))),X4)) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.446.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.446.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X1,equivalent(X3,X2)),X4))),X4)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.446.0.1']),
% 1.07/1.49 [weight('<305,434,14,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.446.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X1,equivalent(X3,X2)),X4))),X4)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.446.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_446]).
% 1.07/1.49 cnf('0.627.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4)),true,is_a_theorem(equivalent(X3,X4)),true),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.5.2.0','0.265.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.627.0.1',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4)),true,is_a_theorem(equivalent(X3,X4)),true) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.627.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.627.1.0',plain,
% 1.07/1.49 ( true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4)),true,is_a_theorem(equivalent(X3,X4)),true) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.627.0.1']),
% 1.07/1.49 [weight('<419,265,5,[0,0,0,1]>')]).
% 1.07/1.49 cnf('0.627.2.0',plain,
% 1.07/1.49 ( ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X4)),true,is_a_theorem(equivalent(X3,X4)),true) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.627.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_627]).
% 1.07/1.49 cnf('0.629.0.0',plain,
% 1.07/1.49 ( true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3),X3)),true) ),
% 1.07/1.49 inference(cp,[status(thm)],['0.627.2.0','0.446.2.0',theory(equality)]),
% 1.07/1.49 [pos('L.1','L')]).
% 1.07/1.49 cnf('0.629.0.1',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3),X3)) ),
% 1.07/1.49 inference(reduction,[status(thm)],['0.629.0.0','0.1.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('0.629.1.0',plain,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3),X3)) ),
% 1.07/1.49 inference(weigh,[status(thm)],['0.629.0.1']),
% 1.07/1.49 [weight('<181,627,446,[1,0,0,1]>')]).
% 1.07/1.49 cnf('0.629.2.0',plain,
% 1.07/1.49 ( is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3),X3)) = true ),
% 1.07/1.49 inference(orient,[status(thm)],['0.629.1.0',theory(equality)]),
% 1.07/1.49 [x,rule_629]).
% 1.07/1.49 cnf('1.0.0.0',conjecture,
% 1.07/1.49 ( true = is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) ),
% 1.07/1.49 file('/tmp/WALDMEISTER_4412_n020',conjecture_1)).
% 1.07/1.49 cnf('1.0.0.1',plain,
% 1.07/1.49 ( true = true ),
% 1.07/1.49 inference(reduction,[status(thm)],['1.0.0.0','0.629.2.0',theory(equality)]),
% 1.07/1.49 [pos('R','L')]).
% 1.07/1.49 cnf('1.0.0.2',plain,
% 1.07/1.49 ( $true ),
% 1.07/1.49 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 1.07/1.49 [conjecture_1]).
% 1.07/1.49
% 1.07/1.49 Proved Goals:
% 1.07/1.49 No. 1: true ?= is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) joined, current: true = true
% 1.07/1.49 1 goal was specified, which was proved.
% 1.07/1.49 % SZS output end CNFRefutation
% 1.07/1.49 #END OF PROOF
% 1.07/1.49
% 1.07/1.49 Problem WALDMEISTER_4412_n020
% 1.07/1.49 CPs.gen 151866
% 1.07/1.49 CPs.reexp 0
% 1.07/1.49 Select 1199
% 1.07/1.49 R 629
% 1.07/1.49 E 0
% 1.07/1.49 vsize 6.6M
% 1.07/1.49 rss 4.1M
% 1.07/1.49 process.time 0.494s
% 1.07/1.49 wallclock.time 0.494s
% 1.07/1.49 status S
% 1.07/1.49
% 1.07/1.49
% 1.07/1.49 Waldmeister states: Goal proved.
% 1.07/1.49 % SZS status Unsatisfiable
%------------------------------------------------------------------------------