TSTP Solution File: LCL385-10 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL385-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n016.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 16:05:35 EDT 2022
% Result : Unsatisfiable 67.09s 67.51s
% Output : CNFRefutation 67.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL385-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n016.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 : Sat Jul 2 14:03:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.96 ********************************************************************************
% 0.57/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.96 * |/ | \/ | *
% 0.57/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.96 * A. Jaeger and B. Loechner | | *
% 0.57/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.96 ********************************************************************************
% 0.57/0.96
% 0.57/0.96
% 0.57/0.96 Goals:
% 0.57/0.96 ------
% 0.57/0.96
% 0.57/0.96 ( 1) true ?=? is_a_theorem(implies(implies(x,not(y)),implies(y,not(x))))
% 0.57/0.96
% 0.57/0.96 Detected structure: Orkus
% 0.57/0.96 ********************************************************************************
% 0.57/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.96 ********************************************************************************
% 0.57/0.96
% 67.09/67.51 joined goal: 1 true ?= is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))) to true
% 67.09/67.51 goal joined
% 67.09/67.51 % SZS status Unsatisfiable
% 67.09/67.51 #START OF PROOF
% 67.09/67.51 % SZS output start CNFRefutation
% 67.09/67.51 cnf('0.1.0.0',axiom,
% 67.09/67.51 ( X1 = ifeq(X2,X2,X1,X3) ),
% 67.09/67.51 file('/tmp/WALDMEISTER_2221_n016')).
% 67.09/67.51 cnf('0.1.1.0',plain,
% 67.09/67.51 ( X1 = ifeq(X2,X2,X1,X3) ),
% 67.09/67.51 inference(weigh,[status(thm)],['0.1.0.0']),
% 67.09/67.51 [weight('<0,0,0,[0,0,0,1]>')]).
% 67.09/67.51 cnf('0.1.2.0',plain,
% 67.09/67.51 ( ifeq(X1,X1,X2,X3) = X2 ),
% 67.09/67.51 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 67.09/67.51 [x,rule_1]).
% 67.09/67.51 cnf('0.2.0.0',axiom,
% 67.09/67.51 ( true = is_a_theorem(implies(X1,implies(not(X1),X2))) ),
% 67.09/67.51 file('/tmp/WALDMEISTER_2221_n016')).
% 67.09/67.51 cnf('0.2.1.0',plain,
% 67.09/67.51 ( true = is_a_theorem(implies(X1,implies(not(X1),X2))) ),
% 67.09/67.51 inference(weigh,[status(thm)],['0.2.0.0']),
% 67.09/67.51 [weight('<1,0,0,[0,0,0,2]>')]).
% 67.09/67.51 cnf('0.2.2.0',plain,
% 67.09/67.51 ( is_a_theorem(implies(X1,implies(not(X1),X2))) = true ),
% 67.09/67.51 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 67.09/67.51 [x,rule_2]).
% 67.09/67.51 cnf('0.3.0.0',axiom,
% 67.09/67.51 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
% 67.09/67.51 file('/tmp/WALDMEISTER_2221_n016')).
% 67.09/67.51 cnf('0.3.1.0',plain,
% 67.09/67.51 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
% 67.09/67.51 inference(weigh,[status(thm)],['0.3.0.0']),
% 67.09/67.51 [weight('<2,0,0,[0,0,0,3]>')]).
% 67.09/67.52 cnf('0.3.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_3]).
% 67.09/67.52 cnf('0.4.0.0',axiom,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),X1),X1)) ),
% 67.09/67.52 file('/tmp/WALDMEISTER_2221_n016')).
% 67.09/67.52 cnf('0.4.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),X1),X1)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.4.0.0']),
% 67.09/67.52 [weight('<3,0,0,[0,0,0,4]>')]).
% 67.09/67.52 cnf('0.4.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(not(X1),X1),X1)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_4]).
% 67.09/67.52 cnf('0.5.0.0',axiom,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 67.09/67.52 file('/tmp/WALDMEISTER_2221_n016')).
% 67.09/67.52 cnf('0.5.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.5.0.0']),
% 67.09/67.52 [weight('<4,0,0,[0,0,0,5]>')]).
% 67.09/67.52 cnf('0.5.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_5]).
% 67.09/67.52 cnf('0.15.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(not(X1),X2)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.15.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(not(X1),X2)),X3)),true,is_a_theorem(X3),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.15.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.15.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(not(X1),X2)),X3)),true,is_a_theorem(X3),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.15.0.1']),
% 67.09/67.52 [weight('<239,5,2,[1,0,0,7]>')]).
% 67.09/67.52 cnf('0.15.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(X1,implies(not(X1),X2)),X3)),true,is_a_theorem(X3),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_15]).
% 67.09/67.52 cnf('0.16.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.15.2.0','0.3.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.16.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.16.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.16.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.16.0.1']),
% 67.09/67.52 [weight('<155,15,3,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.16.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_16]).
% 67.09/67.52 cnf('0.20.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.4.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.20.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X1),X2)),true,is_a_theorem(X2),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.20.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.20.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X1),X2)),true,is_a_theorem(X2),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.20.0.1']),
% 67.09/67.52 [weight('<239,5,4,[1,0,0,7]>')]).
% 67.09/67.52 cnf('0.20.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X1),X2)),true,is_a_theorem(X2),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_20]).
% 67.09/67.52 cnf('0.21.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,X1)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.16.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.21.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,X1)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.21.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.21.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,X1)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.21.0.1']),
% 67.09/67.52 [weight('<29,20,16,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.21.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,X1)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_21]).
% 67.09/67.52 cnf('0.26.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.3.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.26.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.26.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.26.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.26.0.1']),
% 67.09/67.52 [weight('<155,20,3,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.26.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_26]).
% 67.09/67.52 cnf('0.28.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.21.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.28.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.28.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.28.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.28.0.1']),
% 67.09/67.52 [weight('<155,21,5,[0,0,0,7]>')]).
% 67.09/67.52 cnf('0.28.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_28]).
% 67.09/67.52 cnf('0.34.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X1),X2),X3)),true,is_a_theorem(implies(X1,X3)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.16.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.34.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(not(X1),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.34.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.34.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(not(X1),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.34.0.1']),
% 67.09/67.52 [weight('<239,16,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.34.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(not(X1),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_34]).
% 67.09/67.52 cnf('0.35.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,X3),implies(not(X1),X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.34.2.0','0.3.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.35.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(not(X1),X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.35.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.35.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(X2,X3),implies(not(X1),X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.35.0.1']),
% 67.09/67.52 [weight('<155,34,3,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.35.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(not(X1),X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_35]).
% 67.09/67.52 cnf('0.37.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,X3)),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.28.2.0','0.35.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.37.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,X3)),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.37.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.37.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,X3)),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.37.0.1']),
% 67.09/67.52 [weight('<155,35,28,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.37.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,X3)),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_37]).
% 67.09/67.52 cnf('0.38.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(implies(X2,X2)),X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.34.2.0','0.37.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.38.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(not(implies(X2,X2)),X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.38.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(not(implies(X2,X2)),X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.38.0.1']),
% 67.09/67.52 [weight('<109,37,34,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.38.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(not(implies(X2,X2)),X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_38]).
% 67.09/67.52 cnf('0.55.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.55.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.55.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.55.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.55.0.1']),
% 67.09/67.52 [weight('<?,5,3,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.55.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_55]).
% 67.09/67.52 cnf('0.56.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.38.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.56.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.56.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.56.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.56.0.1']),
% 67.09/67.52 [weight('<209,55,38,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.56.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_56]).
% 67.09/67.52 cnf('0.57.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.56.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.57.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.57.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.57.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.57.0.1']),
% 67.09/67.52 [weight('<55,56,20,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.57.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(X2,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_57]).
% 67.09/67.52 cnf('0.59.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.57.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.59.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.59.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.59.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.59.0.1']),
% 67.09/67.52 [weight('<131,57,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.59.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_59]).
% 67.09/67.52 cnf('0.66.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(implies(X3,X2)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.59.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.66.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(implies(X3,X2)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.66.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.66.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(implies(X3,X2)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.66.0.1']),
% 67.09/67.52 [weight('<209,59,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.66.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(implies(X3,X2)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_66]).
% 67.09/67.52 cnf('0.68.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.66.2.0','0.16.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.68.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.68.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.68.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.68.0.1']),
% 67.09/67.52 [weight('<109,66,16,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.68.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_68]).
% 67.09/67.52 cnf('0.69.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.66.2.0','0.26.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.69.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.69.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.69.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.69.0.1']),
% 67.09/67.52 [weight('<109,66,26,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.69.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_69]).
% 67.09/67.52 cnf('0.77.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),implies(X4,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.68.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.77.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),implies(X4,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.77.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.77.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),implies(X4,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.77.0.1']),
% 67.09/67.52 [weight('<209,68,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.77.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),implies(X4,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.77.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_77]).
% 67.09/67.52 cnf('0.79.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X3,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.69.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.79.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X3,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.79.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.79.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X3,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.79.0.1']),
% 67.09/67.52 [weight('<209,69,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.79.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X3,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_79]).
% 67.09/67.52 cnf('0.106.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.106.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.106.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.106.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.106.0.1']),
% 67.09/67.52 [weight('<?,5,3,[1,0,0,7]>')]).
% 67.09/67.52 cnf('0.106.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_106]).
% 67.09/67.52 cnf('0.153.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(not(X3),X2)),X4),implies(X3,X4))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.35.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.153.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(not(X3),X2)),X4),implies(X3,X4))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.153.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.153.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(not(X3),X2)),X4),implies(X3,X4))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.153.0.1']),
% 67.09/67.52 [weight('<271,55,35,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.153.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(X1,X2),implies(not(X3),X2)),X4),implies(X3,X4))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_153]).
% 67.09/67.52 cnf('0.262.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.3.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.262.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.262.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.262.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.262.0.1']),
% 67.09/67.52 [weight('<305,55,3,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.262.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.262.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_262]).
% 67.09/67.52 cnf('0.361.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.16.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.361.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.361.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.361.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.361.0.1']),
% 67.09/67.52 [weight('<?,16,5,[0,0,0,7]>')]).
% 67.09/67.52 cnf('0.361.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X4)),true,is_a_theorem(X4),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.361.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_361]).
% 67.09/67.52 cnf('0.362.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(not(X1),X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.361.2.0','0.153.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.362.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,implies(not(X1),X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.362.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.362.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,implies(not(X1),X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.362.0.1']),
% 67.09/67.52 [weight('<109,361,153,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.362.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(X2,implies(not(X1),X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.362.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_362]).
% 67.09/67.52 cnf('0.363.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.361.2.0','0.262.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.363.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.363.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.363.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.363.0.1']),
% 67.09/67.52 [weight('<155,361,262,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.363.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.363.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_363]).
% 67.09/67.52 cnf('0.368.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(X2,X4))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.362.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.368.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(X2,X4))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.368.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.368.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(X2,X4))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.368.0.1']),
% 67.09/67.52 [weight('<209,362,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.368.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(X2,X4))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.368.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_368]).
% 67.09/67.52 cnf('0.372.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(not(X1),X2),X3),implies(X4,X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.106.2.0','0.368.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.372.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(implies(not(X1),X2),X3),implies(X4,X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.372.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.372.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(implies(not(X1),X2),X3),implies(X4,X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.372.0.1']),
% 67.09/67.52 [weight('<209,368,106,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.372.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(implies(implies(not(X1),X2),X3),implies(X4,X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.372.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_372]).
% 67.09/67.52 cnf('0.374.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,not(X2))),true,is_a_theorem(implies(X2,implies(X1,X3))),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.363.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.374.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,not(X2))),true,is_a_theorem(implies(X2,implies(X1,X3))),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.374.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.374.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,not(X2))),true,is_a_theorem(implies(X2,implies(X1,X3))),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.374.0.1']),
% 67.09/67.52 [weight('<239,363,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.374.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(X1,not(X2))),true,is_a_theorem(implies(X2,implies(X1,X3))),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.374.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_374]).
% 67.09/67.52 cnf('0.381.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(implies(X2,not(X1)),X4))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.363.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.381.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(implies(X2,not(X1)),X4))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.381.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.381.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(implies(X2,not(X1)),X4))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.381.0.1']),
% 67.09/67.52 [weight('<271,363,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.381.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(implies(X2,not(X1)),X4))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.381.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_381]).
% 67.09/67.52 cnf('0.698.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,implies(not(X4),X5)),X2),X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.77.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.698.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,implies(not(X4),X5)),X2),X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.698.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.698.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,implies(not(X4),X5)),X2),X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.698.0.1']),
% 67.09/67.52 [weight('<341,77,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.698.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,implies(not(X4),X5)),X2),X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.698.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_698]).
% 67.09/67.52 cnf('0.699.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.698.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.699.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.699.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.699.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.699.0.1']),
% 67.09/67.52 [weight('<155,698,20,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.699.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.699.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_699]).
% 67.09/67.52 cnf('0.726.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(implies(not(X4),X4),X4),X2),X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.79.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.726.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(implies(not(X4),X4),X4),X2),X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.726.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.726.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(implies(not(X4),X4),X4),X2),X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.726.0.1']),
% 67.09/67.52 [weight('<341,79,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.726.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(implies(not(X4),X4),X4),X2),X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.726.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_726]).
% 67.09/67.52 cnf('0.727.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.726.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.727.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.727.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.727.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.727.0.1']),
% 67.09/67.52 [weight('<155,726,20,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.727.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.727.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_727]).
% 67.09/67.52 cnf('0.1021.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(implies(not(X1),X2),X3),implies(X4,X3)),X5),implies(X1,X5))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.372.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.1021.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(implies(not(X1),X2),X3),implies(X4,X3)),X5),implies(X1,X5))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.1021.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.1021.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(implies(not(X1),X2),X3),implies(X4,X3)),X5),implies(X1,X5))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.1021.0.1']),
% 67.09/67.52 [weight('<341,372,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.1021.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(implies(not(X1),X2),X3),implies(X4,X3)),X5),implies(X1,X5))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.1021.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_1021]).
% 67.09/67.52 cnf('0.1928.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.363.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.1928.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3))),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.1928.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.1928.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3))),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.1928.0.1']),
% 67.09/67.52 [weight('<379,363,5,[0,0,0,7]>')]).
% 67.09/67.52 cnf('0.1928.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3))),X4)),true,is_a_theorem(X4),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.1928.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_1928]).
% 67.09/67.52 cnf('0.2006.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(implies(X2,not(X1)),X4)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.381.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2006.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(implies(X2,not(X1)),X4)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2006.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2006.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(implies(X2,not(X1)),X4)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2006.0.1']),
% 67.09/67.52 [weight('<379,381,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2006.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(implies(X2,not(X1)),X4)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2006.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2006]).
% 67.09/67.52 cnf('0.2462.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.699.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.2462.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2462.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.2462.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3),X4)),true,is_a_theorem(X4),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2462.0.1']),
% 67.09/67.52 [weight('<379,699,5,[0,0,0,7]>')]).
% 67.09/67.52 cnf('0.2462.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(implies(X1,implies(not(X1),X2)),X3),X3),X4)),true,is_a_theorem(X4),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2462.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2462]).
% 67.09/67.52 cnf('0.2463.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X2),X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2462.2.0','0.262.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2463.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X2),X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2463.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2463.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X2),X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2463.0.1']),
% 67.09/67.52 [weight('<155,2462,262,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.2463.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X2),X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2463.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2463]).
% 67.09/67.52 cnf('0.2472.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(implies(X1,X2),X4))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.2463.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2472.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(implies(X1,X2),X4))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2472.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2472.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(implies(X1,X2),X4))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2472.0.1']),
% 67.09/67.52 [weight('<271,2463,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2472.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(implies(X1,X2),X4))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2472.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2472]).
% 67.09/67.52 cnf('0.2475.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(not(implies(not(X1),X2)),X1),implies(not(X1),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.2472.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2475.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(implies(not(X1),X2)),X1),implies(not(X1),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2475.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2475.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(implies(not(X1),X2)),X1),implies(not(X1),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2475.0.1']),
% 67.09/67.52 [weight('<209,2472,20,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2475.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(not(implies(not(X1),X2)),X1),implies(not(X1),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2475.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2475]).
% 67.09/67.52 cnf('0.2523.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(not(implies(not(X1),X2)),X1)),true,is_a_theorem(implies(not(X1),X2)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2475.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2523.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(implies(not(X1),X2)),X1)),true,is_a_theorem(implies(not(X1),X2)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2523.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2523.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(implies(not(X1),X2)),X1)),true,is_a_theorem(implies(not(X1),X2)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2523.0.1']),
% 67.09/67.52 [weight('<305,2475,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2523.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(not(implies(not(X1),X2)),X1)),true,is_a_theorem(implies(not(X1),X2)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2523.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2523]).
% 67.09/67.52 cnf('0.2682.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(X1),X1),X1),X2),X2),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.727.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.2682.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(X1),X1),X1),X2),X2),X3)),true,is_a_theorem(X3),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2682.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.2682.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(X1),X1),X1),X2),X2),X3)),true,is_a_theorem(X3),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2682.0.1']),
% 67.09/67.52 [weight('<379,727,5,[0,0,0,7]>')]).
% 67.09/67.52 cnf('0.2682.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(X1),X1),X1),X2),X2),X3)),true,is_a_theorem(X3),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2682.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2682]).
% 67.09/67.52 cnf('0.2683.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,X1))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2682.2.0','0.1021.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2683.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,X1))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2683.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2683.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(X2,X1))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2683.0.1']),
% 67.09/67.52 [weight('<55,2682,1021,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.2683.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(X2,X1))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2683.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2683]).
% 67.09/67.52 cnf('0.2689.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.2683.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2689.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2689.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2689.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2689.0.1']),
% 67.09/67.52 [weight('<131,2683,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2689.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2689.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2689]).
% 67.09/67.52 cnf('0.2695.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2682.2.0','0.262.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2695.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2695.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2695.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2695.0.1']),
% 67.09/67.52 [weight('<155,2682,262,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.2695.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2695.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2695]).
% 67.09/67.52 cnf('0.2696.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2006.2.0','0.2695.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2696.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2696.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2696.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2696.0.1']),
% 67.09/67.52 [weight('<131,2695,2006,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2696.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2696.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2696]).
% 67.09/67.52 cnf('0.2735.0.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2683.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.3.1','L')]).
% 67.09/67.52 cnf('0.2735.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2735.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R.3','L')]).
% 67.09/67.52 cnf('0.2735.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2735.0.1']),
% 67.09/67.52 [weight('<209,2683,5,[0,0,0,7]>')]).
% 67.09/67.52 cnf('0.2735.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2735.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2735]).
% 67.09/67.52 cnf('0.2742.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2689.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2742.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2742.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2742.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2742.0.1']),
% 67.09/67.52 [weight('<209,2689,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2742.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2742.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2742]).
% 67.09/67.52 cnf('0.2743.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(X1),implies(X1,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2742.2.0','0.2696.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2743.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(X1),implies(X1,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2743.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2743.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(X1),implies(X1,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2743.0.1']),
% 67.09/67.52 [weight('<71,2742,2696,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.2743.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(X1),implies(X1,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2743.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2743]).
% 67.09/67.52 cnf('0.2754.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.2743.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2754.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2754.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2754.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2754.0.1']),
% 67.09/67.52 [weight('<155,2743,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2754.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2754.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2754]).
% 67.09/67.52 cnf('0.2755.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(not(X1)),X1)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.20.2.0','0.2754.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2755.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(not(X1)),X1)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2755.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2755.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(not(X1)),X1)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2755.0.1']),
% 67.09/67.52 [weight('<55,2754,20,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2755.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(not(X1)),X1)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2755.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2755]).
% 67.09/67.52 cnf('0.2903.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2696.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2903.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2903.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2903.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2903.0.1']),
% 67.09/67.52 [weight('<209,2696,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2903.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2903.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2903]).
% 67.09/67.52 cnf('0.2904.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,not(not(X1)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2903.2.0','0.2755.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2904.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,not(not(X1)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2904.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2904.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,not(not(X1)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2904.0.1']),
% 67.09/67.52 [weight('<55,2903,2755,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.2904.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,not(not(X1)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2904.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2904]).
% 67.09/67.52 cnf('0.2906.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,not(not(implies(X2,X1))))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2742.2.0','0.2904.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2906.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,not(not(implies(X2,X1))))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2906.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2906.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,not(not(implies(X2,X1))))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2906.0.1']),
% 67.09/67.52 [weight('<89,2904,2742,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2906.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,not(not(implies(X2,X1))))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2906.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2906]).
% 67.09/67.52 cnf('0.2907.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,not(X2))),X2)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2903.2.0','0.2906.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2907.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,not(X2))),X2)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2907.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2907.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,not(X2))),X2)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2907.0.1']),
% 67.09/67.52 [weight('<89,2906,2903,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2907.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,not(X2))),X2)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2907.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2907]).
% 67.09/67.52 cnf('0.2915.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,X2)),implies(X2,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.374.2.0','0.2906.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2915.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),implies(X2,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2915.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2915.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),implies(X2,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2915.0.1']),
% 67.09/67.52 [weight('<109,2906,374,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2915.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,X2)),implies(X2,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2915.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2915]).
% 67.09/67.52 cnf('0.2916.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,X2)),X1)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2523.2.0','0.2915.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2916.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),X1)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2916.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2916.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),X1)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2916.0.1']),
% 67.09/67.52 [weight('<71,2915,2523,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2916.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,X2)),X1)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2916.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2916]).
% 67.09/67.52 cnf('0.2987.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(not(implies(X1,X3)),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.2916.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.2987.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(not(implies(X1,X3)),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.2987.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.2987.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(not(implies(X1,X3)),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.2987.0.1']),
% 67.09/67.52 [weight('<155,2916,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.2987.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,X2),implies(not(implies(X1,X3)),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.2987.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_2987]).
% 67.09/67.52 cnf('0.3036.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,not(X1))),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.2907.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.3036.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,not(X1))),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.3036.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.3036.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,not(X1))),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.3036.0.1']),
% 67.09/67.52 [weight('<181,2907,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.3036.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,not(X1))),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.3036.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_3036]).
% 67.09/67.52 cnf('0.3037.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,not(X2))),implies(X3,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2735.2.0','0.3036.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.3037.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,not(X2))),implies(X3,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.3037.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.3037.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,not(X2))),implies(X3,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.3037.0.1']),
% 67.09/67.52 [weight('<131,3036,2735,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.3037.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,not(X2))),implies(X3,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.3037.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_3037]).
% 67.09/67.52 cnf('0.3038.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,X2)),not(X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2523.2.0','0.3037.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.3038.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),not(X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.3038.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.3038.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),not(X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.3038.0.1']),
% 67.09/67.52 [weight('<89,3037,2523,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.3038.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,X2)),not(X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.3038.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_3038]).
% 67.09/67.52 cnf('0.3156.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(X3,X1)),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.3038.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.3156.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(X3,X1)),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.3156.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.3156.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(X3,X1)),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.3156.0.1']),
% 67.09/67.52 [weight('<181,3038,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.3156.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(X3,X1)),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.3156.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_3156]).
% 67.09/67.52 cnf('0.4061.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(not(X2),X2))),true,is_a_theorem(implies(X1,X2)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2695.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.4061.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,implies(not(X2),X2))),true,is_a_theorem(implies(X1,X2)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.4061.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.4061.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,implies(not(X2),X2))),true,is_a_theorem(implies(X1,X2)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.4061.0.1']),
% 67.09/67.52 [weight('<239,2695,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.4061.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(X1,implies(not(X2),X2))),true,is_a_theorem(implies(X1,X2)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.4061.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_4061]).
% 67.09/67.52 cnf('0.4072.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.4061.2.0','0.2987.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.4072.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.4072.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.4072.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.4072.0.1']),
% 67.09/67.52 [weight('<131,4061,2987,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.4072.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.4072.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_4072]).
% 67.09/67.52 cnf('0.4092.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),implies(X2,X1)),implies(X2,X1))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.4061.2.0','0.3156.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.4092.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),implies(X2,X1)),implies(X2,X1))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.4092.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.4092.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(not(X1),implies(X2,X1)),implies(X2,X1))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.4092.0.1']),
% 67.09/67.52 [weight('<155,4061,3156,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.4092.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(not(X1),implies(X2,X1)),implies(X2,X1))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.4092.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_4092]).
% 67.09/67.52 cnf('0.4365.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.4072.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.4365.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.4365.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.4365.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.4365.0.1']),
% 67.09/67.52 [weight('<209,4072,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.4365.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.4365.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_4365]).
% 67.09/67.52 cnf('0.5272.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(not(implies(X1,X3)),X2)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.2987.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.5272.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(not(implies(X1,X3)),X2)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.5272.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.5272.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(not(implies(X1,X3)),X2)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.5272.0.1']),
% 67.09/67.52 [weight('<239,2987,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.5272.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(not(implies(X1,X3)),X2)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.5272.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_5272]).
% 67.09/67.52 cnf('0.6478.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(not(X1),implies(X2,X1))),true,is_a_theorem(implies(X2,X1)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.4092.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.6478.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(X1),implies(X2,X1))),true,is_a_theorem(implies(X2,X1)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.6478.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.6478.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(X1),implies(X2,X1))),true,is_a_theorem(implies(X2,X1)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.6478.0.1']),
% 67.09/67.52 [weight('<239,4092,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.6478.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(not(X1),implies(X2,X1))),true,is_a_theorem(implies(X2,X1)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.6478.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_6478]).
% 67.09/67.52 cnf('0.9635.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(not(X1),X2)),true,is_a_theorem(implies(not(implies(X3,X1)),X2)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.3156.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.9635.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(X1),X2)),true,is_a_theorem(implies(not(implies(X3,X1)),X2)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.9635.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.9635.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(not(X1),X2)),true,is_a_theorem(implies(not(implies(X3,X1)),X2)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.9635.0.1']),
% 67.09/67.52 [weight('<271,3156,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.9635.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(not(X1),X2)),true,is_a_theorem(implies(not(implies(X3,X1)),X2)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.9635.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_9635]).
% 67.09/67.52 cnf('0.13644.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(implies(X1,X2),X3)),implies(not(implies(X4,not(X1))),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5272.2.0','0.3036.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13644.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(implies(X1,X2),X3)),implies(not(implies(X4,not(X1))),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13644.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13644.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(implies(X1,X2),X3)),implies(not(implies(X4,not(X1))),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13644.0.1']),
% 67.09/67.52 [weight('<271,5272,3036,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.13644.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(implies(X1,X2),X3)),implies(not(implies(X4,not(X1))),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13644.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13644]).
% 67.09/67.52 cnf('0.13645.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(implies(X1,X2),not(X1))),X2)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.4365.2.0','0.13644.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13645.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(implies(X1,X2),not(X1))),X2)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13645.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13645.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(implies(X1,X2),not(X1))),X2)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13645.0.1']),
% 67.09/67.52 [weight('<131,13644,4365,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13645.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(implies(X1,X2),not(X1))),X2)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13645.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13645]).
% 67.09/67.52 cnf('0.13646.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,not(X1)),not(X2)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2903.2.0','0.13645.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13646.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(X2,not(X1)),not(X2)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13646.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13646.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(X2,not(X1)),not(X2)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13646.0.1']),
% 67.09/67.52 [weight('<131,13645,2903,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13646.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(implies(X2,not(X1)),not(X2)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13646.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13646]).
% 67.09/67.52 cnf('0.13651.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,implies(implies(X2,X3),not(X2)))),X3)),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.9635.2.0','0.13645.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13651.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,implies(implies(X2,X3),not(X2)))),X3)) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13651.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13651.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,implies(implies(X2,X3),not(X2)))),X3)) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13651.0.1']),
% 67.09/67.52 [weight('<181,13645,9635,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13651.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,implies(implies(X2,X3),not(X2)))),X3)) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13651.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13651]).
% 67.09/67.52 cnf('0.13652.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(X1),implies(implies(X2,X1),not(X2)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.2523.2.0','0.13651.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13652.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(X1),implies(implies(X2,X1),not(X2)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13652.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13652.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(X1),implies(implies(X2,X1),not(X2)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13652.0.1']),
% 67.09/67.52 [weight('<131,13651,2523,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13652.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(X1),implies(implies(X2,X1),not(X2)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13652.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13652]).
% 67.09/67.52 cnf('0.13701.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,not(X2)),not(X1)),X3),implies(X2,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.13646.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13701.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,not(X2)),not(X1)),X3),implies(X2,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13701.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13701.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,not(X2)),not(X1)),X3),implies(X2,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13701.0.1']),
% 67.09/67.52 [weight('<239,13646,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13701.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(X1,not(X2)),not(X1)),X3),implies(X2,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13701.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13701]).
% 67.09/67.52 cnf('0.13763.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),not(X1)),X3),implies(not(X2),X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.13652.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13763.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),not(X1)),X3),implies(not(X2),X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13763.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13763.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),not(X1)),X3),implies(not(X2),X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13763.0.1']),
% 67.09/67.52 [weight('<239,13652,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13763.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(X1,X2),not(X1)),X3),implies(not(X2),X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13763.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13763]).
% 67.09/67.52 cnf('0.13764.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(X1),implies(X2,implies(implies(X2,X1),X3)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.1928.2.0','0.13763.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13764.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(X1),implies(X2,implies(implies(X2,X1),X3)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13764.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13764.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(X1),implies(X2,implies(implies(X2,X1),X3)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13764.0.1']),
% 67.09/67.52 [weight('<155,13763,1928,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13764.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(X1),implies(X2,implies(implies(X2,X1),X3)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13764.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13764]).
% 67.09/67.52 cnf('0.13769.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(not(implies(X1,X2)),implies(X3,implies(implies(X3,X2),X4)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.9635.2.0','0.13764.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13769.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),implies(X3,implies(implies(X3,X2),X4)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13769.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13769.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(not(implies(X1,X2)),implies(X3,implies(implies(X3,X2),X4)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13769.0.1']),
% 67.09/67.52 [weight('<209,13764,9635,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13769.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(not(implies(X1,X2)),implies(X3,implies(implies(X3,X2),X4)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13769.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13769]).
% 67.09/67.52 cnf('0.13770.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.6478.2.0','0.13769.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13770.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13770.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13770.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13770.0.1']),
% 67.09/67.52 [weight('<89,13769,6478,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13770.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13770.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13770]).
% 67.09/67.52 cnf('0.13790.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.55.2.0','0.13770.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.13790.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.13790.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.13790.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.13790.0.1']),
% 67.09/67.52 [weight('<181,13770,55,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.13790.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.13790.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_13790]).
% 67.09/67.52 cnf('0.19657.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.5.2.0','0.13790.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.19657.0.1',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.19657.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.19657.1.0',plain,
% 67.09/67.52 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.19657.0.1']),
% 67.09/67.52 [weight('<271,13790,5,[0,0,0,1]>')]).
% 67.09/67.52 cnf('0.19657.2.0',plain,
% 67.09/67.52 ( ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.19657.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_19657]).
% 67.09/67.52 cnf('0.19661.0.0',plain,
% 67.09/67.52 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))),true) ),
% 67.09/67.52 inference(cp,[status(thm)],['0.19657.2.0','0.13701.2.0',theory(equality)]),
% 67.09/67.52 [pos('L.1','L')]).
% 67.09/67.52 cnf('0.19661.0.1',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))) ),
% 67.09/67.52 inference(reduction,[status(thm)],['0.19661.0.0','0.1.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('0.19661.1.0',plain,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))) ),
% 67.09/67.52 inference(weigh,[status(thm)],['0.19661.0.1']),
% 67.09/67.52 [weight('<131,19657,13701,[1,0,0,1]>')]).
% 67.09/67.52 cnf('0.19661.2.0',plain,
% 67.09/67.52 ( is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))) = true ),
% 67.09/67.52 inference(orient,[status(thm)],['0.19661.1.0',theory(equality)]),
% 67.09/67.52 [x,rule_19661]).
% 67.09/67.52 cnf('1.0.0.0',conjecture,
% 67.09/67.52 ( true = is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))) ),
% 67.09/67.52 file('/tmp/WALDMEISTER_2221_n016',conjecture_1)).
% 67.09/67.52 cnf('1.0.0.1',plain,
% 67.09/67.52 ( true = true ),
% 67.09/67.52 inference(reduction,[status(thm)],['1.0.0.0','0.19661.2.0',theory(equality)]),
% 67.09/67.52 [pos('R','L')]).
% 67.09/67.52 cnf('1.0.0.2',plain,
% 67.09/67.52 ( $true ),
% 67.09/67.52 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 67.09/67.52 [conjecture_1]).
% 67.09/67.52
% 67.09/67.52 Proved Goals:
% 67.09/67.52 No. 1: true ?= is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))) joined, current: true = true
% 67.09/67.52 1 goal was specified, which was proved.
% 67.09/67.52 % SZS output end CNFRefutation
% 67.09/67.52 #END OF PROOF
% 67.09/67.52
% 67.09/67.52 Problem WALDMEISTER_2221_n016
% 67.09/67.52 CPs.gen 55513137
% 67.09/67.52 CPs.reexp 0
% 67.09/67.52 Select 87435
% 67.09/67.52 R 19661
% 67.09/67.52 E 0
% 67.09/67.52 vsize 23.1M
% 67.09/67.52 rss 21.3M
% 67.09/67.52 process.time 66.547s
% 67.09/67.52 wallclock.time 66.557s
% 67.09/67.52 status S
% 67.09/67.52
% 67.09/67.52
% 67.09/67.52 Waldmeister states: Goal proved.
% 67.09/67.52 % SZS status Unsatisfiable
%------------------------------------------------------------------------------