TSTP Solution File: LCL113-10 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL113-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 16:03:37 EDT 2022
% Result : Unsatisfiable 4.06s 4.42s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL113-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 10:55:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.65/1.05 ********************************************************************************
% 0.65/1.05 * W A L D M E I S T E R \| \ / \|/ *
% 0.65/1.05 * |/ | \/ | *
% 0.65/1.05 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.65/1.05 * A. Jaeger and B. Loechner | | *
% 0.65/1.05 * <waldmeister@informatik.uni-kl.de> | *
% 0.65/1.05 ********************************************************************************
% 0.65/1.05
% 0.65/1.05
% 0.65/1.05 Goals:
% 0.65/1.05 ------
% 0.65/1.05
% 0.65/1.05 ( 1) true ?=? is_a_theorem(implies(implies(not(a),b),implies(not(b),a)))
% 0.65/1.05
% 0.65/1.05 Detected structure: Orkus
% 0.65/1.05 ********************************************************************************
% 0.65/1.05 ****************************** COMPLETION - PROOF ******************************
% 0.65/1.05 ********************************************************************************
% 0.65/1.05
% 4.06/4.42 joined goal: 1 true ?= is_a_theorem(implies(implies(not(a),b),implies(not(b),a))) to true
% 4.06/4.42 goal joined
% 4.06/4.42 % SZS status Unsatisfiable
% 4.06/4.42 #START OF PROOF
% 4.06/4.42 % SZS output start CNFRefutation
% 4.06/4.42 cnf('0.1.0.0',axiom,
% 4.06/4.42 ( X1 = ifeq(X2,X2,X1,X3) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008')).
% 4.06/4.42 cnf('0.1.1.0',plain,
% 4.06/4.42 ( X1 = ifeq(X2,X2,X1,X3) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.1.0.0']),
% 4.06/4.42 [weight('<0,0,0,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.1.2.0',plain,
% 4.06/4.42 ( ifeq(X1,X1,X2,X3) = X2 ),
% 4.06/4.42 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_1]).
% 4.06/4.42 cnf('0.2.0.0',axiom,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,implies(X2,X1))) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008')).
% 4.06/4.42 cnf('0.2.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,implies(X2,X1))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.2.0.0']),
% 4.06/4.42 [weight('<1,0,0,[0,0,0,2]>')]).
% 4.06/4.42 cnf('0.2.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(X1,implies(X2,X1))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_2]).
% 4.06/4.42 cnf('0.3.0.0',axiom,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008')).
% 4.06/4.42 cnf('0.3.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.3.0.0']),
% 4.06/4.42 [weight('<2,0,0,[0,0,0,3]>')]).
% 4.06/4.42 cnf('0.3.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_3]).
% 4.06/4.42 cnf('0.4.0.0',axiom,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X2),implies(implies(X2,X1),X1))) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008')).
% 4.06/4.42 cnf('0.4.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X2),implies(implies(X2,X1),X1))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.4.0.0']),
% 4.06/4.42 [weight('<3,0,0,[0,0,0,4]>')]).
% 4.06/4.42 cnf('0.4.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,X2),X2),implies(implies(X2,X1),X1))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_4]).
% 4.06/4.42 cnf('0.5.0.0',axiom,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008')).
% 4.06/4.42 cnf('0.5.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.5.0.0']),
% 4.06/4.42 [weight('<4,0,0,[0,0,0,5]>')]).
% 4.06/4.42 cnf('0.5.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_5]).
% 4.06/4.42 cnf('0.6.0.0',axiom,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008')).
% 4.06/4.42 cnf('0.6.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.6.0.0']),
% 4.06/4.42 [weight('<5,0,0,[0,0,0,6]>')]).
% 4.06/4.42 cnf('0.6.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_6]).
% 4.06/4.42 cnf('0.13.0.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.3.1','L')]).
% 4.06/4.42 cnf('0.13.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.13.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R.3','L')]).
% 4.06/4.42 cnf('0.13.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.13.0.1']),
% 4.06/4.42 [weight('<209,6,2,[1,0,0,7]>')]).
% 4.06/4.42 cnf('0.13.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_13]).
% 4.06/4.42 cnf('0.14.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.13.2.0','0.3.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.14.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.14.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.14.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.14.0.1']),
% 4.06/4.42 [weight('<131,13,3,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.14.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_14]).
% 4.06/4.42 cnf('0.20.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.5.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.20.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.20.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.20.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.20.0.1']),
% 4.06/4.42 [weight('<209,6,5,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.20.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(not(X1),not(X2))),true,is_a_theorem(implies(X2,X1)),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_20]).
% 4.06/4.42 cnf('0.21.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.14.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.21.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.21.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.21.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.21.0.1']),
% 4.06/4.42 [weight('<209,14,6,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.21.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_21]).
% 4.06/4.42 cnf('0.22.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(not(X1),implies(X1,X2))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.21.2.0','0.5.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.22.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(not(X1),implies(X1,X2))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.22.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(not(X1),implies(X1,X2))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.22.0.1']),
% 4.06/4.42 [weight('<71,21,5,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.22.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(not(X1),implies(X1,X2))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_22]).
% 4.06/4.42 cnf('0.23.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.21.2.0','0.4.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.23.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.23.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.23.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.23.0.1']),
% 4.06/4.42 [weight('<89,21,4,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.23.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_23]).
% 4.06/4.42 cnf('0.29.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.13.2.0','0.23.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.29.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.29.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.29.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.29.0.1']),
% 4.06/4.42 [weight('<131,23,13,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.29.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_29]).
% 4.06/4.42 cnf('0.30.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(X1,X1)),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.21.2.0','0.29.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.30.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,X1)) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.30.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.30.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,X1)) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.30.0.1']),
% 4.06/4.42 [weight('<29,29,21,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.30.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(X1,X1)) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_30]).
% 4.06/4.42 cnf('0.37.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.23.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.37.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.37.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.37.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.37.0.1']),
% 4.06/4.42 [weight('<155,23,6,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.37.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_37]).
% 4.06/4.42 cnf('0.38.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.37.2.0','0.30.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.38.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X1),X2),X2)) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.38.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X1),X2),X2)) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.38.0.1']),
% 4.06/4.42 [weight('<89,37,30,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.38.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,X1),X2),X2)) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_38]).
% 4.06/4.42 cnf('0.55.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.3.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.55.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.55.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.55.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.55.0.1']),
% 4.06/4.42 [weight('<?,6,3,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.55.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_55]).
% 4.06/4.42 cnf('0.56.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.55.2.0','0.22.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.56.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.56.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.56.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.56.0.1']),
% 4.06/4.42 [weight('<155,55,22,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.56.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X1),X3))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_56]).
% 4.06/4.42 cnf('0.68.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.55.2.0','0.23.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.68.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.68.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.68.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.68.0.1']),
% 4.06/4.42 [weight('<181,55,23,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.68.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_68]).
% 4.06/4.42 cnf('0.151.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(not(X1),X3)),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.56.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.151.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(not(X1),X3)),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.151.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.151.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(not(X1),X3)),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.151.0.1']),
% 4.06/4.42 [weight('<239,56,6,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.151.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(not(X1),X3)),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.151.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_151]).
% 4.06/4.42 cnf('0.153.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(not(not(X1)),implies(X2,X1))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.151.2.0','0.5.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.153.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(not(not(X1)),implies(X2,X1))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.153.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.153.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(not(not(X1)),implies(X2,X1))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.153.0.1']),
% 4.06/4.42 [weight('<89,151,5,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.153.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(not(not(X1)),implies(X2,X1))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_153]).
% 4.06/4.42 cnf('0.188.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(not(X2)),X3))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.55.2.0','0.153.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.188.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(not(X2)),X3))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.188.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.188.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(not(X2)),X3))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.188.0.1']),
% 4.06/4.42 [weight('<181,153,55,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.188.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(not(X2)),X3))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.188.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_188]).
% 4.06/4.42 cnf('0.259.0.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(not(X1),not(X2)),implies(X2,X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.5.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.3.1','L')]).
% 4.06/4.42 cnf('0.259.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(not(X1),not(X2)),implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.259.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R.3','L')]).
% 4.06/4.42 cnf('0.259.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(not(X1),not(X2)),implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.259.0.1']),
% 4.06/4.42 [weight('<?,6,5,[1,0,0,7]>')]).
% 4.06/4.42 cnf('0.259.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(implies(not(X1),not(X2)),implies(X2,X1)),X3)),true,is_a_theorem(X3),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.259.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_259]).
% 4.06/4.42 cnf('0.488.0.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,X1),X2),X2),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.38.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.3.1','L')]).
% 4.06/4.42 cnf('0.488.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,X1),X2),X2),X3)),true,is_a_theorem(X3),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.488.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R.3','L')]).
% 4.06/4.42 cnf('0.488.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(implies(X1,X1),X2),X2),X3)),true,is_a_theorem(X3),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.488.0.1']),
% 4.06/4.42 [weight('<271,38,6,[0,0,0,7]>')]).
% 4.06/4.42 cnf('0.488.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(implies(implies(X1,X1),X2),X2),X3)),true,is_a_theorem(X3),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.488.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_488]).
% 4.06/4.42 cnf('0.489.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(not(not(X1)),X1)),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.488.2.0','0.188.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.489.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(not(not(X1)),X1)) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.489.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.489.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(not(not(X1)),X1)) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.489.0.1']),
% 4.06/4.42 [weight('<55,488,188,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.489.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(not(not(X1)),X1)) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.489.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_489]).
% 4.06/4.42 cnf('0.490.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(X1,not(not(X1)))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.20.2.0','0.489.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.490.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,not(not(X1)))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.490.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.490.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(X1,not(not(X1)))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.490.0.1']),
% 4.06/4.42 [weight('<55,489,20,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.490.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(X1,not(not(X1)))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.490.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_490]).
% 4.06/4.42 cnf('0.914.0.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,not(not(X1))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.490.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.3.1','L')]).
% 4.06/4.42 cnf('0.914.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,not(not(X1))),X2)),true,is_a_theorem(X2),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.914.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R.3','L')]).
% 4.06/4.42 cnf('0.914.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(X1,not(not(X1))),X2)),true,is_a_theorem(X2),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.914.0.1']),
% 4.06/4.42 [weight('<209,490,6,[0,0,0,7]>')]).
% 4.06/4.42 cnf('0.914.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(X1,not(not(X1))),X2)),true,is_a_theorem(X2),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.914.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_914]).
% 4.06/4.42 cnf('0.3873.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.6.2.0','0.68.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.3873.0.1',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.3873.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.3873.1.0',plain,
% 4.06/4.42 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.3873.0.1']),
% 4.06/4.42 [weight('<271,68,6,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.3873.2.0',plain,
% 4.06/4.42 ( ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.3873.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_3873]).
% 4.06/4.42 cnf('0.3931.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.55.2.0','0.3.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.3931.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.3931.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.3931.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.3931.0.1']),
% 4.06/4.42 [weight('<?,55,3,[1,0,0,1]>')]).
% 4.06/4.42 cnf('0.3931.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.3931.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_3931]).
% 4.06/4.42 cnf('0.3939.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.3873.2.0','0.3931.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.3939.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.3939.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.3939.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.3939.0.1']),
% 4.06/4.42 [weight('<181,3931,3873,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.3939.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.3939.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_3939]).
% 4.06/4.42 cnf('0.3940.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.914.2.0','0.3939.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.3940.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.3940.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.3940.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.3940.0.1']),
% 4.06/4.42 [weight('<131,3939,914,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.3940.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.3940.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_3940]).
% 4.06/4.42 cnf('0.4528.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,not(not(X2))),X3),implies(implies(X1,X2),X3))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.55.2.0','0.3940.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.4528.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,not(not(X2))),X3),implies(implies(X1,X2),X3))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.4528.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.4528.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(implies(X1,not(not(X2))),X3),implies(implies(X1,X2),X3))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.4528.0.1']),
% 4.06/4.42 [weight('<239,3940,55,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.4528.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(implies(X1,not(not(X2))),X3),implies(implies(X1,X2),X3))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.4528.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_4528]).
% 4.06/4.42 cnf('0.4529.0.0',plain,
% 4.06/4.42 ( true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))),true) ),
% 4.06/4.42 inference(cp,[status(thm)],['0.259.2.0','0.4528.2.0',theory(equality)]),
% 4.06/4.42 [pos('L.1','L')]).
% 4.06/4.42 cnf('0.4529.0.1',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))) ),
% 4.06/4.42 inference(reduction,[status(thm)],['0.4529.0.0','0.1.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('0.4529.1.0',plain,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))) ),
% 4.06/4.42 inference(weigh,[status(thm)],['0.4529.0.1']),
% 4.06/4.42 [weight('<131,4528,259,[0,0,0,1]>')]).
% 4.06/4.42 cnf('0.4529.2.0',plain,
% 4.06/4.42 ( is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))) = true ),
% 4.06/4.42 inference(orient,[status(thm)],['0.4529.1.0',theory(equality)]),
% 4.06/4.42 [x,rule_4529]).
% 4.06/4.42 cnf('1.0.0.0',conjecture,
% 4.06/4.42 ( true = is_a_theorem(implies(implies(not(a),b),implies(not(b),a))) ),
% 4.06/4.42 file('/tmp/WALDMEISTER_15273_n008',conjecture_1)).
% 4.06/4.42 cnf('1.0.0.1',plain,
% 4.06/4.42 ( true = true ),
% 4.06/4.42 inference(reduction,[status(thm)],['1.0.0.0','0.4529.2.0',theory(equality)]),
% 4.06/4.42 [pos('R','L')]).
% 4.06/4.42 cnf('1.0.0.2',plain,
% 4.06/4.42 ( $true ),
% 4.06/4.42 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 4.06/4.42 [conjecture_1]).
% 4.06/4.42
% 4.06/4.42 Proved Goals:
% 4.06/4.42 No. 1: true ?= is_a_theorem(implies(implies(not(a),b),implies(not(b),a))) joined, current: true = true
% 4.06/4.42 1 goal was specified, which was proved.
% 4.06/4.42 % SZS output end CNFRefutation
% 4.06/4.42 #END OF PROOF
% 4.06/4.42
% 4.06/4.42 Problem WALDMEISTER_15273_n008
% 4.06/4.42 CPs.gen 2992778
% 4.06/4.42 CPs.reexp 0
% 4.06/4.42 Select 8902
% 4.06/4.42 R 4529
% 4.06/4.42 E 0
% 4.06/4.42 vsize 11.7M
% 4.06/4.42 rss 7.0M
% 4.06/4.42 process.time 3.370s
% 4.06/4.42 wallclock.time 3.370s
% 4.06/4.42 status S
% 4.06/4.42
% 4.06/4.42
% 4.06/4.42 Waldmeister states: Goal proved.
% 4.06/4.42 % SZS status Unsatisfiable
%------------------------------------------------------------------------------