TSTP Solution File: LCL109-6 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% 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 16:03:35 EDT 2022
% Result : Unsatisfiable 0.59s 1.07s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 04:06:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.97 * |/ | \/ | *
% 0.57/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.97 * A. Jaeger and B. Loechner | | *
% 0.57/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.57/0.97
% 0.57/0.97 Goals:
% 0.57/0.97 ------
% 0.57/0.97
% 0.57/0.97 ( 1) truth ?=? implies(implies(implies(a,b),implies(b,a)),implies(b,a))
% 0.57/0.97
% 0.57/0.97 Detected structure: AlternativeWajsbergAlgebra
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.59/1.07 joined goal: 1 truth ?= implies(implies(implies(a,b),implies(b,a)),implies(b,a)) to truth
% 0.59/1.07 goal joined
% 0.59/1.07 % SZS status Unsatisfiable
% 0.59/1.07 #START OF PROOF
% 0.59/1.07 % SZS output start CNFRefutation
% 0.59/1.07 cnf('0.1.0.0',axiom,
% 0.59/1.07 ( X1 = xor(X1,falsehood) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.1.1.0',plain,
% 0.59/1.07 ( X1 = xor(X1,falsehood) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.59/1.07 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.59/1.07 cnf('0.1.2.0',plain,
% 0.59/1.07 ( xor(X1,falsehood) = X1 ),
% 0.59/1.07 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_1]).
% 0.59/1.07 cnf('0.2.0.0',axiom,
% 0.59/1.07 ( X1 = and_star(X1,truth) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.2.1.0',plain,
% 0.59/1.07 ( X1 = and_star(X1,truth) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.59/1.07 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.59/1.07 cnf('0.2.2.0',plain,
% 0.59/1.07 ( and_star(X1,truth) = X1 ),
% 0.59/1.07 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_2]).
% 0.59/1.07 cnf('0.3.0.0',axiom,
% 0.59/1.07 ( xor(X1,X2) = xor(X2,X1) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.3.1.0',plain,
% 0.59/1.07 ( xor(X1,X2) = xor(X2,X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.59/1.07 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.59/1.07 cnf('0.3.2.0',plain,
% 0.59/1.07 ( xor(X1,X2) = xor(X2,X1) ),
% 0.59/1.07 inference(activate,[status(thm)],['0.3.1.0']),
% 0.59/1.07 [equation_1]).
% 0.59/1.07 cnf('0.5.0.0',axiom,
% 0.59/1.07 ( xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.5.1.0',plain,
% 0.59/1.07 ( xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.59/1.07 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.59/1.07 cnf('0.5.2.0',plain,
% 0.59/1.07 ( xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_4]).
% 0.59/1.07 cnf('0.6.0.0',axiom,
% 0.59/1.07 ( xor(X1,truth) = not(X1) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.6.1.0',plain,
% 0.59/1.07 ( xor(X1,truth) = not(X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.59/1.07 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.59/1.07 cnf('0.6.2.0',plain,
% 0.59/1.07 ( xor(X1,truth) = not(X1) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_5]).
% 0.59/1.07 cnf('0.7.0.0',axiom,
% 0.59/1.07 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.7.1.0',plain,
% 0.59/1.07 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.59/1.07 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.59/1.07 cnf('0.7.2.0',plain,
% 0.59/1.07 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_6]).
% 0.59/1.07 cnf('0.8.0.0',axiom,
% 0.59/1.07 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.8.1.0',plain,
% 0.59/1.07 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.59/1.07 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.59/1.07 cnf('0.8.2.0',plain,
% 0.59/1.07 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.59/1.07 inference(activate,[status(thm)],['0.8.1.0']),
% 0.59/1.07 [equation_2]).
% 0.59/1.07 cnf('0.9.0.0',axiom,
% 0.59/1.07 ( and_star(X1,and_star(X2,X3)) = and_star(and_star(X1,X2),X3) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.9.1.0',plain,
% 0.59/1.07 ( and_star(X1,and_star(X2,X3)) = and_star(and_star(X1,X2),X3) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.59/1.07 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.59/1.07 cnf('0.9.2.0',plain,
% 0.59/1.07 ( and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_7]).
% 0.59/1.07 cnf('0.10.0.0',axiom,
% 0.59/1.07 ( and_star(X1,falsehood) = falsehood ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.10.1.0',plain,
% 0.59/1.07 ( and_star(X1,falsehood) = falsehood ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.59/1.07 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.59/1.07 cnf('0.10.2.0',plain,
% 0.59/1.07 ( and_star(X1,falsehood) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_8]).
% 0.59/1.07 cnf('0.12.0.0',axiom,
% 0.59/1.07 ( and_star(xor(truth,X1),X1) = falsehood ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.12.1.0',plain,
% 0.59/1.07 ( and_star(xor(truth,X1),X1) = falsehood ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.59/1.07 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.59/1.07 cnf('0.12.1.1',plain,
% 0.59/1.07 ( and_star(X1,xor(truth,X1)) = falsehood ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.12.1.0','0.8.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.12.2.0',plain,
% 0.59/1.07 ( and_star(X1,xor(truth,X1)) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.12.1.1',theory(equality)]),
% 0.59/1.07 [u,rule_9]).
% 0.59/1.07 cnf('0.13.0.0',axiom,
% 0.59/1.07 ( falsehood = not(truth) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.13.1.0',plain,
% 0.59/1.07 ( falsehood = not(truth) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.59/1.07 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.59/1.07 cnf('0.13.2.0',plain,
% 0.59/1.07 ( not(truth) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_10]).
% 0.59/1.07 cnf('0.14.0.0',plain,
% 0.59/1.07 ( xor(falsehood,X1) = X1 ),
% 0.59/1.07 inference(cp,[status(thm)],['0.3.2.0','0.1.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.14.1.0',plain,
% 0.59/1.07 ( xor(falsehood,X1) = X1 ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.59/1.07 [weight('<19,3,1,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.14.2.0',plain,
% 0.59/1.07 ( xor(falsehood,X1) = X1 ),
% 0.59/1.07 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_11]).
% 0.59/1.07 cnf('0.15.0.0',plain,
% 0.59/1.07 ( truth = not(falsehood) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.14.2.0','0.6.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.15.1.0',plain,
% 0.59/1.07 ( truth = not(falsehood) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.59/1.07 [weight('<11,14,6,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.15.2.0',plain,
% 0.59/1.07 ( not(falsehood) = truth ),
% 0.59/1.07 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_12]).
% 0.59/1.07 cnf('0.16.0.0',plain,
% 0.59/1.07 ( and_star(truth,X1) = X1 ),
% 0.59/1.07 inference(cp,[status(thm)],['0.8.2.0','0.2.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.16.1.0',plain,
% 0.59/1.07 ( and_star(truth,X1) = X1 ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.59/1.07 [weight('<19,8,2,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.16.2.0',plain,
% 0.59/1.07 ( and_star(truth,X1) = X1 ),
% 0.59/1.07 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_13]).
% 0.59/1.07 cnf('0.17.0.0',plain,
% 0.59/1.07 ( falsehood = and_star(falsehood,X1) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.10.2.0','0.8.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.17.1.0',plain,
% 0.59/1.07 ( falsehood = and_star(falsehood,X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.59/1.07 [weight('<19,10,8,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.17.2.0',plain,
% 0.59/1.07 ( and_star(falsehood,X1) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_14]).
% 0.59/1.07 cnf('0.20.0.0',plain,
% 0.59/1.07 ( not(X1) = xor(truth,X1) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.6.2.0','0.3.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.20.1.0',plain,
% 0.59/1.07 ( not(X1) = xor(truth,X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.59/1.07 [weight('<23,6,3,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.20.2.0',plain,
% 0.59/1.07 ( xor(truth,X1) = not(X1) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_17]).
% 0.59/1.07 cnf('0.21.0.0',plain,
% 0.59/1.07 ( and_star(X1,xor(truth,X1)) = falsehood ),
% 0.59/1.07 inference(interreduction_right,[status(thm)],['0.12.2.0'])).
% 0.59/1.07 cnf('0.21.0.1',plain,
% 0.59/1.07 ( and_star(X1,not(X1)) = falsehood ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.21.0.0','0.20.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.21.1.0',plain,
% 0.59/1.07 ( and_star(X1,not(X1)) = falsehood ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.21.0.1']),
% 0.59/1.07 [weight('<29,12,20,[0,0,0,0]>')]).
% 0.59/1.07 cnf('0.21.2.0',plain,
% 0.59/1.07 ( and_star(X1,not(X1)) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_18]).
% 0.59/1.07 cnf('0.22.0.0',plain,
% 0.59/1.07 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(interreduction_right,[status(thm)],['0.7.2.0'])).
% 0.59/1.07 cnf('0.22.0.1',plain,
% 0.59/1.07 ( not(and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.22.0.0','0.20.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.22.0.2',plain,
% 0.59/1.07 ( not(and_star(X1,not(X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.22.0.1','0.20.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1.2','L')]).
% 0.59/1.07 cnf('0.22.1.0',plain,
% 0.59/1.07 ( not(and_star(X1,not(X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.22.0.2']),
% 0.59/1.07 [weight('<53,7,20,[0,0,0,0]>')]).
% 0.59/1.07 cnf('0.22.2.0',plain,
% 0.59/1.07 ( not(and_star(X1,not(X2))) = implies(X1,X2) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_19]).
% 0.59/1.07 cnf('0.25.0.0',plain,
% 0.59/1.07 ( implies(truth,X1) = not(not(X1)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.22.2.0','0.16.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.25.1.0',plain,
% 0.59/1.07 ( implies(truth,X1) = not(not(X1)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.59/1.07 [weight('<27,22,16,[1,0,0,1]>')]).
% 0.59/1.07 cnf('0.25.2.0',plain,
% 0.59/1.07 ( not(not(X1)) = implies(truth,X1) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_22]).
% 0.59/1.07 cnf('0.27.0.0',plain,
% 0.59/1.07 ( implies(X1,X2) = not(and_star(not(X2),X1)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.22.2.0','0.8.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.27.1.0',plain,
% 0.59/1.07 ( implies(X1,X2) = not(and_star(not(X2),X1)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.27.0.0']),
% 0.59/1.07 [weight('<53,22,8,[1,0,0,1]>')]).
% 0.59/1.07 cnf('0.27.2.0',plain,
% 0.59/1.07 ( not(and_star(not(X1),X2)) = implies(X2,X1) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_24]).
% 0.59/1.07 cnf('0.29.0.0',plain,
% 0.59/1.07 ( and_star(X1,and_star(not(X1),X2)) = and_star(falsehood,X2) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.9.2.0','0.21.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.29.0.1',plain,
% 0.59/1.07 ( and_star(X1,and_star(not(X1),X2)) = falsehood ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.29.0.0','0.17.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.29.1.0',plain,
% 0.59/1.07 ( and_star(X1,and_star(not(X1),X2)) = falsehood ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.29.0.1']),
% 0.59/1.07 [weight('<55,21,9,[0,0,0,1]>')]).
% 0.59/1.07 cnf('0.29.2.0',plain,
% 0.59/1.07 ( and_star(X1,and_star(not(X1),X2)) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_26]).
% 0.59/1.07 cnf('0.32.0.0',plain,
% 0.59/1.07 ( xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/1.07 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.59/1.07 cnf('0.32.0.1',plain,
% 0.59/1.07 ( xor(not(X1),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.32.0.0','0.6.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.32.1.0',plain,
% 0.59/1.07 ( xor(not(X1),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.32.0.1']),
% 0.59/1.07 [weight('<59,5,6,[0,0,0,0]>')]).
% 0.59/1.07 cnf('0.32.1.1',plain,
% 0.59/1.07 ( xor(not(X1),X2) = xor(X1,not(X2)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.32.1.0','0.20.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.32.2.0',plain,
% 0.59/1.07 ( xor(not(X1),X2) = xor(X1,not(X2)) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.32.1.1',theory(equality)]),
% 0.59/1.07 [u,rule_29]).
% 0.59/1.07 cnf('0.33.0.0',plain,
% 0.59/1.07 ( xor(X1,not(truth)) = not(not(X1)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.32.2.0','0.6.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.33.0.1',plain,
% 0.59/1.07 ( xor(X1,falsehood) = not(not(X1)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.33.0.0','0.13.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.33.0.2',plain,
% 0.59/1.07 ( X1 = not(not(X1)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.33.0.1','0.1.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.33.0.3',plain,
% 0.59/1.07 ( X1 = implies(truth,X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.33.0.2','0.25.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.33.1.0',plain,
% 0.59/1.07 ( X1 = implies(truth,X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.33.0.3']),
% 0.59/1.07 [weight('<19,32,6,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.33.2.0',plain,
% 0.59/1.07 ( implies(truth,X1) = X1 ),
% 0.59/1.07 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_30]).
% 0.59/1.07 cnf('0.34.0.0',plain,
% 0.59/1.07 ( not(not(X1)) = implies(truth,X1) ),
% 0.59/1.07 inference(interreduction_right,[status(thm)],['0.25.2.0'])).
% 0.59/1.07 cnf('0.34.0.1',plain,
% 0.59/1.07 ( not(not(X1)) = X1 ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.34.0.0','0.33.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.34.1.0',plain,
% 0.59/1.07 ( not(not(X1)) = X1 ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.34.0.1']),
% 0.59/1.07 [weight('<19,25,33,[0,0,0,0]>')]).
% 0.59/1.07 cnf('0.34.2.0',plain,
% 0.59/1.07 ( not(not(X1)) = X1 ),
% 0.59/1.07 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_31]).
% 0.59/1.07 cnf('0.35.0.0',plain,
% 0.59/1.07 ( implies(X1,not(X2)) = not(and_star(X1,X2)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.22.2.0','0.34.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1.2','L')]).
% 0.59/1.07 cnf('0.35.1.0',plain,
% 0.59/1.07 ( implies(X1,not(X2)) = not(and_star(X1,X2)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.59/1.07 [weight('<44,34,22,[0,0,0,3]>')]).
% 0.59/1.07 cnf('0.35.2.0',plain,
% 0.59/1.07 ( not(and_star(X1,X2)) = implies(X1,not(X2)) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_32]).
% 0.59/1.07 cnf('0.37.0.0',plain,
% 0.59/1.07 ( not(and_star(not(X1),X2)) = implies(X2,X1) ),
% 0.59/1.07 inference(interreduction_right,[status(thm)],['0.27.2.0'])).
% 0.59/1.07 cnf('0.37.0.1',plain,
% 0.59/1.07 ( implies(not(X1),not(X2)) = implies(X2,X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.37.0.0','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.37.1.0',plain,
% 0.59/1.07 ( implies(not(X1),not(X2)) = implies(X2,X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.37.0.1']),
% 0.59/1.07 [weight('<53,27,35,[0,0,0,0]>')]).
% 0.59/1.07 cnf('0.37.2.0',plain,
% 0.59/1.07 ( implies(not(X1),not(X2)) = implies(X2,X1) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_34]).
% 0.59/1.07 cnf('0.38.0.0',plain,
% 0.59/1.07 ( and_star(X1,X2) = not(implies(X1,not(X2))) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.34.2.0','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.38.1.0',plain,
% 0.59/1.07 ( and_star(X1,X2) = not(implies(X1,not(X2))) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.59/1.07 [weight('<53,35,34,[0,0,0,1]>')]).
% 0.59/1.07 cnf('0.38.2.0',plain,
% 0.59/1.07 ( not(implies(X1,not(X2))) = and_star(X1,X2) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_35]).
% 0.59/1.07 cnf('0.39.0.0',plain,
% 0.59/1.07 ( and_star(X1,not(X2)) = not(implies(X1,X2)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.38.2.0','0.34.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1.2','L')]).
% 0.59/1.07 cnf('0.39.1.0',plain,
% 0.59/1.07 ( and_star(X1,not(X2)) = not(implies(X1,X2)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.59/1.07 [weight('<44,38,34,[1,0,0,3]>')]).
% 0.59/1.07 cnf('0.39.2.0',plain,
% 0.59/1.07 ( not(implies(X1,X2)) = and_star(X1,not(X2)) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_36]).
% 0.59/1.07 cnf('0.40.0.0',plain,
% 0.59/1.07 ( falsehood = and_star(not(X1),and_star(X1,X2)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.29.2.0','0.34.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2.1','L')]).
% 0.59/1.07 cnf('0.40.1.0',plain,
% 0.59/1.07 ( falsehood = and_star(not(X1),and_star(X1,X2)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.59/1.07 [weight('<55,34,29,[0,0,0,3]>')]).
% 0.59/1.07 cnf('0.40.2.0',plain,
% 0.59/1.07 ( and_star(not(X1),and_star(X1,X2)) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_37]).
% 0.59/1.07 cnf('0.41.0.0',plain,
% 0.59/1.07 ( implies(not(X1),not(and_star(X1,X2))) = not(falsehood) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.35.2.0','0.40.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.41.0.1',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),X1) = not(falsehood) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.41.0.0','0.37.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.41.0.2',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),X1) = truth ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.41.0.1','0.15.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.41.1.0',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),X1) = truth ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.41.0.2']),
% 0.59/1.07 [weight('<41,40,35,[0,0,0,1]>')]).
% 0.59/1.07 cnf('0.41.2.0',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),X1) = truth ),
% 0.59/1.07 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_38]).
% 0.59/1.07 cnf('0.52.0.0',plain,
% 0.59/1.07 ( falsehood = and_star(X1,and_star(X2,not(and_star(X1,X2)))) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.21.2.0','0.9.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.52.1.0',plain,
% 0.59/1.07 ( falsehood = and_star(X1,and_star(X2,not(and_star(X1,X2)))) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.52.0.0']),
% 0.59/1.07 [weight('<89,21,9,[1,0,0,0]>')]).
% 0.59/1.07 cnf('0.52.1.1',plain,
% 0.59/1.07 ( falsehood = and_star(X1,and_star(X2,implies(X1,not(X2)))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.52.1.0','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2.2','L')]).
% 0.59/1.07 cnf('0.52.2.0',plain,
% 0.59/1.07 ( and_star(X1,and_star(X2,implies(X1,not(X2)))) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.52.1.1',theory(equality)]),
% 0.59/1.07 [x,rule_46]).
% 0.59/1.07 cnf('0.59.0.0',axiom,
% 0.59/1.07 ( and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 file('/tmp/WALDMEISTER_9283_n019')).
% 0.59/1.07 cnf('0.59.1.0',plain,
% 0.59/1.07 ( and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.59.0.0']),
% 0.59/1.07 [weight('<0,0,0,[0,0,0,11]>')]).
% 0.59/1.07 cnf('0.59.1.1',plain,
% 0.59/1.07 ( and_star(X2,xor(and_star(xor(truth,X1),X2),truth)) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.0','0.8.2.0',theory(equality)]),
% 0.59/1.07 [pos('L','L')]).
% 0.59/1.07 cnf('0.59.1.2',plain,
% 0.59/1.07 ( and_star(X2,not(and_star(xor(truth,X1),X2))) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.1','0.6.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.59.1.3',plain,
% 0.59/1.07 ( and_star(X2,implies(xor(truth,X1),not(X2))) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.2','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.59.1.4',plain,
% 0.59/1.07 ( and_star(X2,implies(not(X1),not(X2))) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.3','0.20.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2.1','L')]).
% 0.59/1.07 cnf('0.59.1.5',plain,
% 0.59/1.07 ( and_star(X2,implies(X2,X1)) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.4','0.37.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.59.1.6',plain,
% 0.59/1.07 ( and_star(X2,implies(X2,X1)) = and_star(X1,xor(and_star(xor(truth,X2),X1),truth)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.5','0.8.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.59.1.7',plain,
% 0.59/1.07 ( and_star(X2,implies(X2,X1)) = and_star(X1,not(and_star(xor(truth,X2),X1))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.6','0.6.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.59.1.8',plain,
% 0.59/1.07 ( and_star(X2,implies(X2,X1)) = and_star(X1,implies(xor(truth,X2),not(X1))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.7','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.59.1.9',plain,
% 0.59/1.07 ( and_star(X2,implies(X2,X1)) = and_star(X1,implies(not(X2),not(X1))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.8','0.20.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2.1','L')]).
% 0.59/1.07 cnf('0.59.1.10',plain,
% 0.59/1.07 ( and_star(X2,implies(X2,X1)) = and_star(X1,implies(X1,X2)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.59.1.9','0.37.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.59.2.0',plain,
% 0.59/1.07 ( and_star(X1,implies(X1,X2)) = and_star(X2,implies(X2,X1)) ),
% 0.59/1.07 inference(activate,[status(thm)],['0.59.1.10']),
% 0.59/1.07 [equation_7]).
% 0.59/1.07 cnf('0.61.0.0',plain,
% 0.59/1.07 ( and_star(X1,implies(X1,and_star(X1,X2))) = and_star(and_star(X1,X2),truth) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.59.2.0','0.41.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.61.0.1',plain,
% 0.59/1.07 ( and_star(X1,implies(X1,and_star(X1,X2))) = and_star(X1,and_star(X2,truth)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.61.0.0','0.9.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.61.0.2',plain,
% 0.59/1.07 ( and_star(X1,implies(X1,and_star(X1,X2))) = and_star(X1,X2) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.61.0.1','0.2.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.61.1.0',plain,
% 0.59/1.07 ( and_star(X1,implies(X1,and_star(X1,X2))) = and_star(X1,X2) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.61.0.2']),
% 0.59/1.07 [weight('<87,59,41,[1,0,0,2]>')]).
% 0.59/1.07 cnf('0.61.2.0',plain,
% 0.59/1.07 ( and_star(X1,implies(X1,and_star(X1,X2))) = and_star(X1,X2) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_54]).
% 0.59/1.07 cnf('0.67.0.0',plain,
% 0.59/1.07 ( falsehood = and_star(X1,and_star(not(X2),implies(X1,X2))) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.52.2.0','0.34.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2.2.2','L')]).
% 0.59/1.07 cnf('0.67.1.0',plain,
% 0.59/1.07 ( falsehood = and_star(X1,and_star(not(X2),implies(X1,X2))) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.67.0.0']),
% 0.59/1.07 [weight('<89,52,34,[1,0,0,6]>')]).
% 0.59/1.07 cnf('0.67.2.0',plain,
% 0.59/1.07 ( and_star(X1,and_star(not(X2),implies(X1,X2))) = falsehood ),
% 0.59/1.07 inference(orient,[status(thm)],['0.67.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_60]).
% 0.59/1.07 cnf('0.68.0.0',plain,
% 0.59/1.07 ( implies(X1,not(and_star(not(X2),implies(X1,X2)))) = not(falsehood) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.35.2.0','0.67.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.68.0.1',plain,
% 0.59/1.07 ( implies(X1,implies(not(X2),not(implies(X1,X2)))) = not(falsehood) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.68.0.0','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.68.0.2',plain,
% 0.59/1.07 ( implies(X1,implies(implies(X1,X2),X2)) = not(falsehood) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.68.0.1','0.37.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.68.0.3',plain,
% 0.59/1.07 ( implies(X1,implies(implies(X1,X2),X2)) = truth ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.68.0.2','0.15.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.68.1.0',plain,
% 0.59/1.07 ( implies(X1,implies(implies(X1,X2),X2)) = truth ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.68.0.3']),
% 0.59/1.07 [weight('<71,67,35,[0,0,0,1]>')]).
% 0.59/1.07 cnf('0.68.2.0',plain,
% 0.59/1.07 ( implies(X1,implies(implies(X1,X2),X2)) = truth ),
% 0.59/1.07 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_61]).
% 0.59/1.07 cnf('0.75.0.0',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),not(X3)) = not(and_star(X1,and_star(X2,X3))) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.35.2.0','0.9.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.75.0.1',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),not(X3)) = implies(X1,not(and_star(X2,X3))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.75.0.0','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.75.0.2',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),not(X3)) = implies(X1,implies(X2,not(X3))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.75.0.1','0.35.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.75.1.0',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),not(X3)) = implies(X1,implies(X2,not(X3))) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.75.0.2']),
% 0.59/1.07 [weight('<90,35,9,[1,0,0,1]>')]).
% 0.59/1.07 cnf('0.75.2.0',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),not(X3)) = implies(X1,implies(X2,not(X3))) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 0.59/1.07 [u,rule_68]).
% 0.59/1.07 cnf('0.76.0.0',plain,
% 0.59/1.07 ( implies(X1,implies(X2,not(not(X3)))) = implies(and_star(X1,X2),X3) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.75.2.0','0.34.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2','L')]).
% 0.59/1.07 cnf('0.76.0.1',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(and_star(X1,X2),X3) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.76.0.0','0.34.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.2.2','L')]).
% 0.59/1.07 cnf('0.76.1.0',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(and_star(X1,X2),X3) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.76.0.1']),
% 0.59/1.07 [weight('<65,75,34,[1,0,0,4]>')]).
% 0.59/1.07 cnf('0.76.2.0',plain,
% 0.59/1.07 ( implies(and_star(X1,X2),X3) = implies(X1,implies(X2,X3)) ),
% 0.59/1.07 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 0.59/1.07 [x,rule_69]).
% 0.59/1.07 cnf('0.82.0.0',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(and_star(X2,not(X3)),not(X1)) ),
% 0.59/1.07 inference(cp,[status(thm)],['0.37.2.0','0.39.2.0',theory(equality)]),
% 0.59/1.07 [pos('L.1','L')]).
% 0.59/1.07 cnf('0.82.1.0',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(and_star(X2,not(X3)),not(X1)) ),
% 0.59/1.07 inference(weigh,[status(thm)],['0.82.0.0']),
% 0.59/1.07 [weight('<103,39,37,[0,0,0,1]>')]).
% 0.59/1.07 cnf('0.82.1.1',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(X2,implies(not(X3),not(X1))) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.82.1.0','0.76.2.0',theory(equality)]),
% 0.59/1.07 [pos('R','L')]).
% 0.59/1.07 cnf('0.82.1.2',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 0.59/1.07 inference(reduction,[status(thm)],['0.82.1.1','0.37.2.0',theory(equality)]),
% 0.59/1.07 [pos('R.2','L')]).
% 0.59/1.07 cnf('0.82.2.0',plain,
% 0.59/1.07 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 0.59/1.07 inference(activate,[status(thm)],['0.82.1.2']),
% 0.59/1.07 [equation_8]).
% 0.59/1.07 cnf('0.83.0.0',plain,
% 0.59/1.07 ( implies(implies(X1,X2),X3) = implies(not(X3),and_star(X1,not(X2))) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.37.2.0','0.39.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.83.1.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X3) = implies(not(X3),and_star(X1,not(X2))) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.83.0.0']),
% 0.59/1.08 [weight('<103,39,37,[0,0,0,3]>')]).
% 0.59/1.08 cnf('0.83.2.0',plain,
% 0.59/1.08 ( implies(not(X1),and_star(X2,not(X3))) = implies(implies(X2,X3),X1) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.83.1.0',theory(equality)]),
% 0.59/1.08 [x,rule_75]).
% 0.59/1.08 cnf('0.84.0.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X3) = implies(not(X3),and_star(not(X2),X1)) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.83.2.0','0.8.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.84.1.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X3) = implies(not(X3),and_star(not(X2),X1)) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.84.0.0']),
% 0.59/1.08 [weight('<103,83,8,[1,0,0,3]>')]).
% 0.59/1.08 cnf('0.84.2.0',plain,
% 0.59/1.08 ( implies(not(X1),and_star(not(X2),X3)) = implies(implies(X3,X2),X1) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.84.1.0',theory(equality)]),
% 0.59/1.08 [x,rule_76]).
% 0.59/1.08 cnf('0.93.0.0',plain,
% 0.59/1.08 ( implies(X1,not(implies(X1,and_star(X1,X2)))) = not(and_star(X1,X2)) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.35.2.0','0.61.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.1','L')]).
% 0.59/1.08 cnf('0.93.0.1',plain,
% 0.59/1.08 ( implies(X1,and_star(X1,not(and_star(X1,X2)))) = not(and_star(X1,X2)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.93.0.0','0.39.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.93.0.2',plain,
% 0.59/1.08 ( implies(X1,and_star(X1,implies(X1,not(X2)))) = not(and_star(X1,X2)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.93.0.1','0.35.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2.2','L')]).
% 0.59/1.08 cnf('0.93.0.3',plain,
% 0.59/1.08 ( implies(X1,and_star(X1,implies(X1,not(X2)))) = implies(X1,not(X2)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.93.0.2','0.35.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('0.93.1.0',plain,
% 0.59/1.08 ( implies(X1,and_star(X1,implies(X1,not(X2)))) = implies(X1,not(X2)) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.93.0.3']),
% 0.59/1.08 [weight('<116,61,35,[0,0,0,1]>')]).
% 0.59/1.08 cnf('0.93.2.0',plain,
% 0.59/1.08 ( implies(X1,and_star(X1,implies(X1,not(X2)))) = implies(X1,not(X2)) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.93.1.0',theory(equality)]),
% 0.59/1.08 [u,rule_85]).
% 0.59/1.08 cnf('0.94.0.0',plain,
% 0.59/1.08 ( implies(X1,not(not(X2))) = implies(X1,and_star(X1,implies(X1,X2))) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.93.2.0','0.34.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2.2.2','L')]).
% 0.59/1.08 cnf('0.94.0.1',plain,
% 0.59/1.08 ( implies(X1,X2) = implies(X1,and_star(X1,implies(X1,X2))) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.94.0.0','0.34.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.94.1.0',plain,
% 0.59/1.08 ( implies(X1,X2) = implies(X1,and_star(X1,implies(X1,X2))) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.94.0.1']),
% 0.59/1.08 [weight('<87,93,34,[1,0,0,6]>')]).
% 0.59/1.08 cnf('0.94.2.0',plain,
% 0.59/1.08 ( implies(X1,and_star(X1,implies(X1,X2))) = implies(X1,X2) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 0.59/1.08 [x,rule_86]).
% 0.59/1.08 cnf('0.96.0.0',plain,
% 0.59/1.08 ( implies(X1,X2) = implies(X1,and_star(X2,implies(X2,X1))) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.94.2.0','0.59.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.96.1.0',plain,
% 0.59/1.08 ( implies(X1,X2) = implies(X1,and_star(X2,implies(X2,X1))) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.96.0.0']),
% 0.59/1.08 [weight('<87,94,59,[1,0,0,2]>')]).
% 0.59/1.08 cnf('0.96.2.0',plain,
% 0.59/1.08 ( implies(X1,and_star(X2,implies(X2,X1))) = implies(X1,X2) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.96.1.0',theory(equality)]),
% 0.59/1.08 [x,rule_88]).
% 0.59/1.08 cnf('0.97.0.0',plain,
% 0.59/1.08 ( implies(not(X1),not(X2)) = implies(not(X1),and_star(not(X2),implies(X1,X2))) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.96.2.0','0.37.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2.2','L')]).
% 0.59/1.08 cnf('0.97.0.1',plain,
% 0.59/1.08 ( implies(X2,X1) = implies(not(X1),and_star(not(X2),implies(X1,X2))) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.97.0.0','0.37.2.0',theory(equality)]),
% 0.59/1.08 [pos('L','L')]).
% 0.59/1.08 cnf('0.97.0.2',plain,
% 0.59/1.08 ( implies(X2,X1) = implies(implies(implies(X1,X2),X2),X1) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.97.0.1','0.84.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('0.97.1.0',plain,
% 0.59/1.08 ( implies(X2,X1) = implies(implies(implies(X1,X2),X2),X1) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.97.0.2']),
% 0.59/1.08 [weight('<87,96,37,[1,0,0,4]>')]).
% 0.59/1.08 cnf('0.97.2.0',plain,
% 0.59/1.08 ( implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.97.1.0',theory(equality)]),
% 0.59/1.08 [x,rule_89]).
% 0.59/1.08 cnf('0.100.0.0',plain,
% 0.59/1.08 ( and_star(X1,implies(X1,implies(implies(X1,X2),X2))) = and_star(implies(implies(X1,X2),X2),implies(X2,X1)) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.59.2.0','0.97.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.100.0.1',plain,
% 0.59/1.08 ( and_star(X1,truth) = and_star(implies(implies(X1,X2),X2),implies(X2,X1)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.100.0.0','0.68.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.100.0.2',plain,
% 0.59/1.08 ( X1 = and_star(implies(implies(X1,X2),X2),implies(X2,X1)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.100.0.1','0.2.2.0',theory(equality)]),
% 0.59/1.08 [pos('L','L')]).
% 0.59/1.08 cnf('0.100.1.0',plain,
% 0.59/1.08 ( X1 = and_star(implies(implies(X1,X2),X2),implies(X2,X1)) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.100.0.2']),
% 0.59/1.08 [weight('<109,97,59,[0,0,0,2]>')]).
% 0.59/1.08 cnf('0.100.1.1',plain,
% 0.59/1.08 ( X1 = and_star(implies(X2,X1),implies(implies(X1,X2),X2)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.100.1.0','0.8.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('0.100.2.0',plain,
% 0.59/1.08 ( and_star(implies(X1,X2),implies(implies(X2,X1),X1)) = X2 ),
% 0.59/1.08 inference(orient,[status(thm)],['0.100.1.1',theory(equality)]),
% 0.59/1.08 [x,rule_92]).
% 0.59/1.08 cnf('0.102.0.0',plain,
% 0.59/1.08 ( X1 = and_star(implies(and_star(X2,implies(X2,X1)),X1),implies(implies(X1,X2),and_star(X2,implies(X2,X1)))) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.100.2.0','0.96.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2.1','L')]).
% 0.59/1.08 cnf('0.102.0.1',plain,
% 0.59/1.08 ( X1 = and_star(implies(X2,implies(implies(X2,X1),X1)),implies(implies(X1,X2),and_star(X2,implies(X2,X1)))) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.102.0.0','0.76.2.0',theory(equality)]),
% 0.59/1.08 [pos('R.1','L')]).
% 0.59/1.08 cnf('0.102.0.2',plain,
% 0.59/1.08 ( X1 = and_star(truth,implies(implies(X1,X2),and_star(X2,implies(X2,X1)))) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.102.0.1','0.68.2.0',theory(equality)]),
% 0.59/1.08 [pos('R.1','L')]).
% 0.59/1.08 cnf('0.102.0.3',plain,
% 0.59/1.08 ( X1 = implies(implies(X1,X2),and_star(X2,implies(X2,X1))) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.102.0.2','0.16.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('0.102.1.0',plain,
% 0.59/1.08 ( X1 = implies(implies(X1,X2),and_star(X2,implies(X2,X1))) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.102.0.3']),
% 0.59/1.08 [weight('<109,100,96,[1,0,0,5]>')]).
% 0.59/1.08 cnf('0.102.2.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),and_star(X2,implies(X2,X1))) = X1 ),
% 0.59/1.08 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 0.59/1.08 [x,rule_94]).
% 0.59/1.08 cnf('0.124.0.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X2) = and_star(truth,implies(implies(implies(implies(X1,X2),X2),X1),X1)) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.100.2.0','0.68.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.1','L')]).
% 0.59/1.08 cnf('0.124.0.1',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X2) = implies(implies(implies(implies(X1,X2),X2),X1),X1) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.124.0.0','0.16.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('0.124.0.2',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.124.0.1','0.97.2.0',theory(equality)]),
% 0.59/1.08 [pos('R.1','L')]).
% 0.59/1.08 cnf('0.124.1.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.124.0.2']),
% 0.59/1.08 [weight('<120,100,68,[1,0,0,1]>')]).
% 0.59/1.08 cnf('0.124.2.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 0.59/1.08 inference(activate,[status(thm)],['0.124.1.0']),
% 0.59/1.08 [equation_11]).
% 0.59/1.08 cnf('0.214.0.0',plain,
% 0.59/1.08 ( implies(X1,implies(X2,and_star(X1,implies(X1,X3)))) = implies(X2,implies(X1,X3)) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.82.2.0','0.94.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.214.1.0',plain,
% 0.59/1.08 ( implies(X1,implies(X2,and_star(X1,implies(X1,X3)))) = implies(X2,implies(X1,X3)) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.214.0.0']),
% 0.59/1.08 [weight('<149,94,82,[0,0,0,2]>')]).
% 0.59/1.08 cnf('0.214.2.0',plain,
% 0.59/1.08 ( implies(X1,implies(X2,and_star(X1,implies(X1,X3)))) = implies(X2,implies(X1,X3)) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.214.1.0',theory(equality)]),
% 0.59/1.08 [u,rule_195]).
% 0.59/1.08 cnf('0.215.0.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),implies(X2,X1)) = implies(X2,X1) ),
% 0.59/1.08 inference(cp,[status(thm)],['0.214.2.0','0.102.2.0',theory(equality)]),
% 0.59/1.08 [pos('L.2','L')]).
% 0.59/1.08 cnf('0.215.1.0',plain,
% 0.59/1.08 ( implies(implies(X1,X2),implies(X2,X1)) = implies(X2,X1) ),
% 0.59/1.08 inference(weigh,[status(thm)],['0.215.0.0']),
% 0.59/1.08 [weight('<87,214,102,[1,0,0,2]>')]).
% 0.59/1.08 cnf('0.215.1.1',plain,
% 0.59/1.08 ( implies(X2,implies(implies(X1,X2),X1)) = implies(X2,X1) ),
% 0.59/1.08 inference(reduction,[status(thm)],['0.215.1.0','0.82.2.0',theory(equality)]),
% 0.59/1.08 [pos('L','L')]).
% 0.59/1.08 cnf('0.215.2.0',plain,
% 0.59/1.08 ( implies(X1,implies(implies(X2,X1),X2)) = implies(X1,X2) ),
% 0.59/1.08 inference(orient,[status(thm)],['0.215.1.1',theory(equality)]),
% 0.59/1.08 [u,rule_196]).
% 0.59/1.08 cnf('1.0.0.0',conjecture,
% 0.59/1.08 ( truth = implies(implies(implies(a,b),implies(b,a)),implies(b,a)) ),
% 0.59/1.08 file('/tmp/WALDMEISTER_9283_n019',conjecture_1)).
% 0.59/1.08 cnf('1.0.0.1',plain,
% 0.59/1.08 ( truth = implies(implies(implies(b,a),implies(a,b)),implies(a,b)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['1.0.0.0','0.124.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('1.0.0.2',plain,
% 0.59/1.08 ( truth = implies(implies(a,implies(implies(b,a),b)),implies(a,b)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['1.0.0.1','0.82.2.0',theory(equality)]),
% 0.59/1.08 [pos('R.1','L')]).
% 0.59/1.08 cnf('1.0.0.3',plain,
% 0.59/1.08 ( truth = implies(a,implies(implies(a,implies(implies(b,a),b)),b)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['1.0.0.2','0.82.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('1.0.0.4',plain,
% 0.59/1.08 ( truth = implies(a,implies(implies(a,b),b)) ),
% 0.59/1.08 inference(reduction,[status(thm)],['1.0.0.3','0.215.2.0',theory(equality)]),
% 0.59/1.08 [pos('R.2.1','L')]).
% 0.59/1.08 cnf('1.0.0.5',plain,
% 0.59/1.08 ( truth = truth ),
% 0.59/1.08 inference(reduction,[status(thm)],['1.0.0.4','0.68.2.0',theory(equality)]),
% 0.59/1.08 [pos('R','L')]).
% 0.59/1.08 cnf('1.0.0.6',plain,
% 0.59/1.08 ( $true ),
% 0.59/1.08 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 0.59/1.08 [conjecture_1]).
% 0.59/1.08
% 0.59/1.08 Proved Goals:
% 0.59/1.08 No. 1: truth ?= implies(implies(implies(a,b),implies(b,a)),implies(b,a)) joined, current: truth = truth
% 0.59/1.08 1 goal was specified, which was proved.
% 0.59/1.08 % SZS output end CNFRefutation
% 0.59/1.08 #END OF PROOF
% 0.59/1.08
% 0.59/1.08 Problem WALDMEISTER_9283_n019
% 0.59/1.08 CPs.gen 20083
% 0.59/1.08 CPs.reexp 0
% 0.59/1.08 Select 2126
% 0.59/1.08 R 196
% 0.59/1.08 E 19
% 0.59/1.08 vsize 6.5M
% 0.59/1.08 rss 4.1M
% 0.59/1.08 process.time 0.107s
% 0.59/1.08 wallclock.time 0.107s
% 0.59/1.08 status S
% 0.59/1.08
% 0.59/1.08
% 0.59/1.08 Waldmeister states: Goal proved.
% 0.59/1.08 % SZS status Unsatisfiable
%------------------------------------------------------------------------------