TSTP Solution File: LCL026-10 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL026-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n019.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 16:03:03 EDT 2022
% Result : Unsatisfiable 1.00s 1.41s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL026-10 : TPTP v8.1.0. Released v7.3.0.
% 0.00/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 13:53:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.98 * |/ | \/ | *
% 0.59/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.98 * A. Jaeger and B. Loechner | | *
% 0.59/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 0.59/0.98
% 0.59/0.98 Goals:
% 0.59/0.98 ------
% 0.59/0.98
% 0.59/0.98 ( 1) true ?=? is_a_theorem(implies(implies(implies(a,b),a),a))
% 0.59/0.98
% 0.59/0.98 Detected structure: Orkus
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 1.00/1.41 joined goal: 1 true ?= is_a_theorem(implies(implies(implies(a,b),a),a)) to true
% 1.00/1.41 goal joined
% 1.00/1.41 % SZS status Unsatisfiable
% 1.00/1.41 #START OF PROOF
% 1.00/1.41 % SZS output start CNFRefutation
% 1.00/1.41 cnf('0.1.0.0',axiom,
% 1.00/1.41 ( X1 = ifeq(X2,X2,X1,X3) ),
% 1.00/1.41 file('/tmp/WALDMEISTER_16029_n019')).
% 1.00/1.41 cnf('0.1.1.0',plain,
% 1.00/1.41 ( X1 = ifeq(X2,X2,X1,X3) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.00/1.41 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.1.2.0',plain,
% 1.00/1.41 ( ifeq(X1,X1,X2,X3) = X2 ),
% 1.00/1.41 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_1]).
% 1.00/1.41 cnf('0.2.0.0',axiom,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(X2,X1))) ),
% 1.00/1.41 file('/tmp/WALDMEISTER_16029_n019')).
% 1.00/1.41 cnf('0.2.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(X2,X1))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.2.0.0']),
% 1.00/1.41 [weight('<1,0,0,[0,0,0,2]>')]).
% 1.00/1.41 cnf('0.2.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(X2,X1))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_2]).
% 1.00/1.41 cnf('0.3.0.0',axiom,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))) ),
% 1.00/1.41 file('/tmp/WALDMEISTER_16029_n019')).
% 1.00/1.41 cnf('0.3.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.00/1.41 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.00/1.41 cnf('0.3.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_3]).
% 1.00/1.41 cnf('0.4.0.0',axiom,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,falsehood),falsehood),X1)) ),
% 1.00/1.41 file('/tmp/WALDMEISTER_16029_n019')).
% 1.00/1.41 cnf('0.4.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,falsehood),falsehood),X1)) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.4.0.0']),
% 1.00/1.41 [weight('<3,0,0,[0,0,0,4]>')]).
% 1.00/1.41 cnf('0.4.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,falsehood),falsehood),X1)) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_4]).
% 1.00/1.41 cnf('0.5.0.0',axiom,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 1.00/1.41 file('/tmp/WALDMEISTER_16029_n019')).
% 1.00/1.41 cnf('0.5.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.00/1.41 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.00/1.41 cnf('0.5.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_5]).
% 1.00/1.41 cnf('0.6.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,X1)),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.6.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,X1)),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.6.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.6.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,X1)),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.6.0.1']),
% 1.00/1.41 [weight('<109,5,2,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.6.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,X1)),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_6]).
% 1.00/1.41 cnf('0.8.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.8.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.8.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.8.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.8.0.1']),
% 1.00/1.41 [weight('<89,6,2,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.8.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_8]).
% 1.00/1.41 cnf('0.9.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,falsehood),falsehood),X2))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.4.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.9.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(implies(X2,falsehood),falsehood),X2))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.9.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.9.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(implies(X2,falsehood),falsehood),X2))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.9.0.1']),
% 1.00/1.41 [weight('<131,6,4,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.9.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(implies(implies(X2,falsehood),falsehood),X2))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_9]).
% 1.00/1.41 cnf('0.21.0.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.3.1','L')]).
% 1.00/1.41 cnf('0.21.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.21.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R.3','L')]).
% 1.00/1.41 cnf('0.21.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.21.0.1']),
% 1.00/1.41 [weight('<209,5,2,[1,0,0,7]>')]).
% 1.00/1.41 cnf('0.21.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_21]).
% 1.00/1.41 cnf('0.22.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X1,X1))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.21.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.22.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,X1))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.22.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,X1))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.22.0.1']),
% 1.00/1.41 [weight('<89,21,3,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.22.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,X2),implies(X1,X1))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_22]).
% 1.00/1.41 cnf('0.23.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,X1)),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.21.2.0','0.22.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.23.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,X1)) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.23.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.23.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,X1)) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.23.0.1']),
% 1.00/1.41 [weight('<29,22,21,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.23.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,X1)) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_23]).
% 1.00/1.41 cnf('0.28.0.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.23.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.3.1','L')]).
% 1.00/1.41 cnf('0.28.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.28.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R.3','L')]).
% 1.00/1.41 cnf('0.28.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.28.0.1']),
% 1.00/1.41 [weight('<155,23,5,[0,0,0,7]>')]).
% 1.00/1.41 cnf('0.28.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_28]).
% 1.00/1.41 cnf('0.30.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.28.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.30.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.30.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.30.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.30.0.1']),
% 1.00/1.41 [weight('<181,28,3,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.30.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_30]).
% 1.00/1.41 cnf('0.38.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(implies(X2,X3),X3)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.30.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.38.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(implies(X2,X3),X3)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.38.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(implies(X2,X3),X3)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.38.0.1']),
% 1.00/1.41 [weight('<239,30,6,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.38.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(implies(X2,X3),X3)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_38]).
% 1.00/1.41 cnf('0.41.0.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,X2))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.8.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.3.1','L')]).
% 1.00/1.41 cnf('0.41.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,X2))),X4)),true,is_a_theorem(X4),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.41.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R.3','L')]).
% 1.00/1.41 cnf('0.41.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,X2))),X4)),true,is_a_theorem(X4),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.41.0.1']),
% 1.00/1.41 [weight('<271,8,5,[0,0,0,7]>')]).
% 1.00/1.41 cnf('0.41.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,X2))),X4)),true,is_a_theorem(X4),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_41]).
% 1.00/1.41 cnf('0.44.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.41.2.0','0.30.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.44.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.44.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.44.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.44.0.1']),
% 1.00/1.41 [weight('<131,41,30,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.44.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_44]).
% 1.00/1.41 cnf('0.49.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X2)),X4),X4))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.44.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.49.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X2)),X4),X4))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.49.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.49.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X2)),X4),X4))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.49.0.1']),
% 1.00/1.41 [weight('<181,44,6,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.49.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X2)),X4),X4))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_49]).
% 1.00/1.41 cnf('0.55.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(X2,X3))),true,is_a_theorem(implies(implies(X1,X2),implies(X1,X3))),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.55.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(X2,X3))),true,is_a_theorem(implies(implies(X1,X2),implies(X1,X3))),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.55.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.55.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(X2,X3))),true,is_a_theorem(implies(implies(X1,X2),implies(X1,X3))),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.55.0.1']),
% 1.00/1.41 [weight('<?,5,3,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.55.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(X1,implies(X2,X3))),true,is_a_theorem(implies(implies(X1,X2),implies(X1,X3))),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_55]).
% 1.00/1.41 cnf('0.63.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(implies(X2,falsehood),falsehood)),implies(X1,X2))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.55.2.0','0.9.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.63.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,falsehood),falsehood)),implies(X1,X2))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.63.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.63.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,falsehood),falsehood)),implies(X1,X2))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.63.0.1']),
% 1.00/1.41 [weight('<181,55,9,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.63.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,implies(implies(X2,falsehood),falsehood)),implies(X1,X2))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_63]).
% 1.00/1.41 cnf('0.64.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(falsehood,X1)),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.21.2.0','0.63.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.64.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(falsehood,X1)) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.64.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.64.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(falsehood,X1)) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.64.0.1']),
% 1.00/1.41 [weight('<29,63,21,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.64.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(falsehood,X1)) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_64]).
% 1.00/1.41 cnf('0.65.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(falsehood,X2))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.64.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.65.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(falsehood,X2))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.65.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.65.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(falsehood,X2))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.65.0.1']),
% 1.00/1.41 [weight('<55,64,6,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.65.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(falsehood,X2))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_65]).
% 1.00/1.41 cnf('0.68.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,falsehood),implies(X1,X2))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.55.2.0','0.65.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.68.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,falsehood),implies(X1,X2))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.68.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.68.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,falsehood),implies(X1,X2))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.68.0.1']),
% 1.00/1.41 [weight('<89,65,55,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.68.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,falsehood),implies(X1,X2))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_68]).
% 1.00/1.41 cnf('0.71.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,falsehood),implies(X2,X3)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.68.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.71.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(X2,falsehood),implies(X2,X3)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.71.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.71.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(X2,falsehood),implies(X2,X3)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.71.0.1']),
% 1.00/1.41 [weight('<131,68,6,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.71.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(implies(X2,falsehood),implies(X2,X3)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_71]).
% 1.00/1.41 cnf('0.86.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X2,falsehood)),implies(X1,implies(X2,X3)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.55.2.0','0.71.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.86.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(X2,falsehood)),implies(X1,implies(X2,X3)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.86.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.86.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(X2,falsehood)),implies(X1,implies(X2,X3)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.86.0.1']),
% 1.00/1.41 [weight('<181,71,55,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.86.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,implies(X2,falsehood)),implies(X1,implies(X2,X3)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.86.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_86]).
% 1.00/1.41 cnf('0.106.0.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.3.1','L')]).
% 1.00/1.41 cnf('0.106.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.106.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R.3','L')]).
% 1.00/1.41 cnf('0.106.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.106.0.1']),
% 1.00/1.41 [weight('<?,5,3,[1,0,0,7]>')]).
% 1.00/1.41 cnf('0.106.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_106]).
% 1.00/1.41 cnf('0.131.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(implies(X2,implies(X3,X2)),X4)),implies(X1,X4))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.55.2.0','0.49.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.131.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,implies(X3,X2)),X4)),implies(X1,X4))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.131.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.131.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,implies(X3,X2)),X4)),implies(X1,X4))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.131.0.1']),
% 1.00/1.41 [weight('<239,55,49,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.131.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,implies(implies(X2,implies(X3,X2)),X4)),implies(X1,X4))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.131.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_131]).
% 1.00/1.41 cnf('0.132.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(implies(X2,X1),X3)),implies(X1,X3))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.106.2.0','0.131.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.132.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,X1),X3)),implies(X1,X3))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.132.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.132.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,X1),X3)),implies(X1,X3))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.132.0.1']),
% 1.00/1.41 [weight('<181,131,106,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.132.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,implies(implies(X2,X1),X3)),implies(X1,X3))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.132.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_132]).
% 1.00/1.41 cnf('0.357.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(implies(X2,falsehood),falsehood))),true,is_a_theorem(implies(X1,X2)),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.63.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.357.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(implies(X2,falsehood),falsehood))),true,is_a_theorem(implies(X1,X2)),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.357.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.357.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(implies(X2,falsehood),falsehood))),true,is_a_theorem(implies(X1,X2)),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.357.0.1']),
% 1.00/1.41 [weight('<271,63,5,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.357.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(X1,implies(implies(X2,falsehood),falsehood))),true,is_a_theorem(implies(X1,X2)),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.357.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_357]).
% 1.00/1.41 cnf('0.358.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,falsehood),X1),X1)),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.357.2.0','0.30.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.358.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,falsehood),X1),X1)) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.358.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.358.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,falsehood),X1),X1)) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.358.0.1']),
% 1.00/1.41 [weight('<89,357,30,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.358.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,falsehood),X1),X1)) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.358.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_358]).
% 1.00/1.41 cnf('0.362.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,falsehood),X1)),true,is_a_theorem(X1),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.358.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.362.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,falsehood),X1)),true,is_a_theorem(X1),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.362.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.362.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(implies(X1,falsehood),X1)),true,is_a_theorem(X1),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.362.0.1']),
% 1.00/1.41 [weight('<155,358,5,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.362.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(implies(X1,falsehood),X1)),true,is_a_theorem(X1),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.362.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_362]).
% 1.00/1.41 cnf('0.434.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(X2,falsehood))),true,is_a_theorem(implies(X1,implies(X2,X3))),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.86.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.434.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(X2,falsehood))),true,is_a_theorem(implies(X1,implies(X2,X3))),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.434.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.434.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(X2,falsehood))),true,is_a_theorem(implies(X1,implies(X2,X3))),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.434.0.1']),
% 1.00/1.41 [weight('<271,86,5,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.434.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(X1,implies(X2,falsehood))),true,is_a_theorem(implies(X1,implies(X2,X3))),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.434.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_434]).
% 1.00/1.41 cnf('0.437.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(implies(X2,X1),falsehood)),implies(X1,X3))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.434.2.0','0.132.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.437.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,X1),falsehood)),implies(X1,X3))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.437.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.437.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,implies(implies(X2,X1),falsehood)),implies(X1,X3))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.437.0.1']),
% 1.00/1.41 [weight('<181,434,132,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.437.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,implies(implies(X2,X1),falsehood)),implies(X1,X3))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.437.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_437]).
% 1.00/1.41 cnf('0.452.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X2,implies(implies(X3,X2),falsehood)),implies(X2,X4)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.437.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.452.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(X2,implies(implies(X3,X2),falsehood)),implies(X2,X4)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.452.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.452.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(X2,implies(implies(X3,X2),falsehood)),implies(X2,X4)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.452.0.1']),
% 1.00/1.41 [weight('<239,437,6,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.452.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(implies(X2,implies(implies(X3,X2),falsehood)),implies(X2,X4)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.452.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_452]).
% 1.00/1.41 cnf('0.492.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,implies(implies(X2,X1),X3))),true,is_a_theorem(implies(X1,X3)),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.132.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.492.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(implies(X2,X1),X3))),true,is_a_theorem(implies(X1,X3)),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.492.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.492.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,implies(implies(X2,X1),X3))),true,is_a_theorem(implies(X1,X3)),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.492.0.1']),
% 1.00/1.41 [weight('<271,132,5,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.492.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(X1,implies(implies(X2,X1),X3))),true,is_a_theorem(implies(X1,X3)),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.492.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_492]).
% 1.00/1.41 cnf('0.493.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.492.2.0','0.38.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.493.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.493.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.493.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.493.0.1']),
% 1.00/1.41 [weight('<89,492,38,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.493.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.493.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_493]).
% 1.00/1.41 cnf('0.496.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(X2,X3))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.492.2.0','0.452.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.496.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(X2,X3))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.496.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.496.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(X2,X3))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.496.0.1']),
% 1.00/1.41 [weight('<131,492,452,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.496.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(X2,X3))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.496.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_496]).
% 1.00/1.41 cnf('0.497.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.6.2.0','0.493.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.497.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.497.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.497.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.497.0.1']),
% 1.00/1.41 [weight('<131,493,6,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.497.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.497.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_497]).
% 1.00/1.41 cnf('0.518.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(X1,implies(implies(X2,X3),X3)))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.55.2.0','0.497.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.518.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,implies(implies(X2,X3),X3)))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.518.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.518.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(X1,X2),implies(X1,implies(implies(X2,X3),X3)))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.518.0.1']),
% 1.00/1.41 [weight('<181,497,55,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.518.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(X1,X2),implies(X1,implies(implies(X2,X3),X3)))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.518.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_518]).
% 1.00/1.41 cnf('0.924.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X1,implies(implies(X2,X3),X3))),true),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.5.2.0','0.518.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.924.0.1',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X1,implies(implies(X2,X3),X3))),true) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.924.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.924.1.0',plain,
% 1.00/1.41 ( true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X1,implies(implies(X2,X3),X3))),true) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.924.0.1']),
% 1.00/1.41 [weight('<271,518,5,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.924.2.0',plain,
% 1.00/1.41 ( ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X1,implies(implies(X2,X3),X3))),true) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.924.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_924]).
% 1.00/1.41 cnf('0.933.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(implies(implies(X2,X3),X4),X4))),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.924.2.0','0.496.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.933.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(implies(implies(X2,X3),X4),X4))) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.933.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.933.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(implies(implies(X2,X3),X4),X4))) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.933.0.1']),
% 1.00/1.41 [weight('<239,924,496,[1,0,0,1]>')]).
% 1.00/1.41 cnf('0.933.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(implies(implies(X2,X3),X4),X4))) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.933.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_933]).
% 1.00/1.41 cnf('0.934.0.0',plain,
% 1.00/1.41 ( true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),true) ),
% 1.00/1.41 inference(cp,[status(thm)],['0.362.2.0','0.933.2.0',theory(equality)]),
% 1.00/1.41 [pos('L.1','L')]).
% 1.00/1.41 cnf('0.934.0.1',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) ),
% 1.00/1.41 inference(reduction,[status(thm)],['0.934.0.0','0.1.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('0.934.1.0',plain,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) ),
% 1.00/1.41 inference(weigh,[status(thm)],['0.934.0.1']),
% 1.00/1.41 [weight('<89,933,362,[0,0,0,1]>')]).
% 1.00/1.41 cnf('0.934.2.0',plain,
% 1.00/1.41 ( is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true ),
% 1.00/1.41 inference(orient,[status(thm)],['0.934.1.0',theory(equality)]),
% 1.00/1.41 [x,rule_934]).
% 1.00/1.41 cnf('1.0.0.0',conjecture,
% 1.00/1.41 ( true = is_a_theorem(implies(implies(implies(a,b),a),a)) ),
% 1.00/1.41 file('/tmp/WALDMEISTER_16029_n019',conjecture_1)).
% 1.00/1.41 cnf('1.0.0.1',plain,
% 1.00/1.41 ( true = true ),
% 1.00/1.41 inference(reduction,[status(thm)],['1.0.0.0','0.934.2.0',theory(equality)]),
% 1.00/1.41 [pos('R','L')]).
% 1.00/1.41 cnf('1.0.0.2',plain,
% 1.00/1.41 ( $true ),
% 1.00/1.41 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 1.00/1.41 [conjecture_1]).
% 1.00/1.41
% 1.00/1.41 Proved Goals:
% 1.00/1.41 No. 1: true ?= is_a_theorem(implies(implies(implies(a,b),a),a)) joined, current: true = true
% 1.00/1.41 1 goal was specified, which was proved.
% 1.00/1.41 % SZS output end CNFRefutation
% 1.00/1.41 #END OF PROOF
% 1.00/1.41
% 1.00/1.41 Problem WALDMEISTER_16029_n019
% 1.00/1.41 CPs.gen 338255
% 1.00/1.41 CPs.reexp 0
% 1.00/1.41 Select 1619
% 1.00/1.41 R 934
% 1.00/1.41 E 0
% 1.00/1.41 vsize 6.8M
% 1.00/1.41 rss 4.1M
% 1.00/1.41 process.time 0.430s
% 1.00/1.41 wallclock.time 0.431s
% 1.00/1.41 status S
% 1.00/1.41
% 1.00/1.41
% 1.00/1.41 Waldmeister states: Goal proved.
% 1.00/1.41 % SZS status Unsatisfiable
%------------------------------------------------------------------------------