TSTP Solution File: LCL148-10 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL148-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n010.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 16:03:51 EDT 2022
% Result : Unsatisfiable 36.18s 36.59s
% Output : CNFRefutation 36.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL148-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : woody %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 3 02:31:33 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.56/0.95 ********************************************************************************
% 0.56/0.95 * W A L D M E I S T E R \| \ / \|/ *
% 0.56/0.95 * |/ | \/ | *
% 0.56/0.95 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.56/0.95 * A. Jaeger and B. Loechner | | *
% 0.56/0.95 * <waldmeister@informatik.uni-kl.de> | *
% 0.56/0.95 ********************************************************************************
% 0.56/0.95
% 0.56/0.95
% 0.56/0.95 Goals:
% 0.56/0.95 ------
% 0.56/0.95
% 0.56/0.95 ( 1) implies(x,big_hat(y,z)) ?=? big_hat(implies(x,y),implies(x,z))
% 0.56/0.95
% 0.56/0.95 Detected structure: WajsbergAlgebra
% 0.56/0.95 ********************************************************************************
% 0.56/0.95 ****************************** COMPLETION - PROOF ******************************
% 0.56/0.95 ********************************************************************************
% 0.56/0.95
% 36.18/36.59 joined goal: 1 implies(x,big_hat(y,z)) ?= big_hat(implies(x,y),implies(x,z)) to implies(x,big_hat(y,z))
% 36.18/36.59 goal joined
% 36.18/36.59 % SZS status Unsatisfiable
% 36.18/36.59 #START OF PROOF
% 36.18/36.59 % SZS output start CNFRefutation
% 36.18/36.59 cnf('0.1.0.0',axiom,
% 36.18/36.59 ( X1 = implies(truth,X1) ),
% 36.18/36.59 file('/tmp/WALDMEISTER_26554_n010')).
% 36.18/36.59 cnf('0.1.1.0',plain,
% 36.18/36.59 ( X1 = implies(truth,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.1.0.0']),
% 36.18/36.59 [weight('<0,0,0,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.1.2.0',plain,
% 36.18/36.59 ( implies(truth,X1) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_1]).
% 36.18/36.59 cnf('0.4.0.0',axiom,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 36.18/36.59 file('/tmp/WALDMEISTER_26554_n010')).
% 36.18/36.59 cnf('0.4.1.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.4.0.0']),
% 36.18/36.59 [weight('<3,0,0,[0,0,0,4]>')]).
% 36.18/36.59 cnf('0.4.2.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 36.18/36.59 inference(activate,[status(thm)],['0.4.1.0']),
% 36.18/36.59 [equation_1]).
% 36.18/36.59 cnf('0.5.0.0',axiom,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = big_V(X1,X2) ),
% 36.18/36.59 file('/tmp/WALDMEISTER_26554_n010')).
% 36.18/36.59 cnf('0.5.1.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = big_V(X1,X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.5.0.0']),
% 36.18/36.59 [weight('<4,0,0,[0,0,0,5]>')]).
% 36.18/36.59 cnf('0.5.2.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = big_V(X1,X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_4]).
% 36.18/36.59 cnf('0.6.0.0',axiom,
% 36.18/36.59 ( implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 36.18/36.59 file('/tmp/WALDMEISTER_26554_n010')).
% 36.18/36.59 cnf('0.6.1.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.6.0.0']),
% 36.18/36.59 [weight('<5,0,0,[0,0,0,6]>')]).
% 36.18/36.59 cnf('0.6.2.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_5]).
% 36.18/36.59 cnf('0.7.0.0',axiom,
% 36.18/36.59 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 36.18/36.59 file('/tmp/WALDMEISTER_26554_n010')).
% 36.18/36.59 cnf('0.7.1.0',plain,
% 36.18/36.59 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.7.0.0']),
% 36.18/36.59 [weight('<6,0,0,[0,0,0,7]>')]).
% 36.18/36.59 cnf('0.7.2.0',plain,
% 36.18/36.59 ( implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_6]).
% 36.18/36.59 cnf('0.9.0.0',axiom,
% 36.18/36.59 ( not(big_V(not(X1),not(X2))) = big_hat(X1,X2) ),
% 36.18/36.59 file('/tmp/WALDMEISTER_26554_n010')).
% 36.18/36.59 cnf('0.9.1.0',plain,
% 36.18/36.59 ( not(big_V(not(X1),not(X2))) = big_hat(X1,X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.9.0.0']),
% 36.18/36.59 [weight('<8,0,0,[0,0,0,9]>')]).
% 36.18/36.59 cnf('0.9.2.0',plain,
% 36.18/36.59 ( not(big_V(not(X1),not(X2))) = big_hat(X1,X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_8]).
% 36.18/36.59 cnf('0.11.0.0',plain,
% 36.18/36.59 ( big_V(truth,X1) = implies(X1,X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.11.1.0',plain,
% 36.18/36.59 ( big_V(truth,X1) = implies(X1,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.11.0.0']),
% 36.18/36.59 [weight('<27,5,1,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.11.2.0',plain,
% 36.18/36.59 ( implies(X1,X1) = big_V(truth,X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_10]).
% 36.18/36.59 cnf('0.13.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,implies(implies(X1,X2),implies(truth,X2))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.13.0.1',plain,
% 36.18/36.59 ( truth = implies(X1,implies(implies(X1,X2),X2)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.13.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.2.2','L')]).
% 36.18/36.59 cnf('0.13.0.2',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X1,X2)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.13.0.1','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.2','L')]).
% 36.18/36.59 cnf('0.13.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.13.0.2']),
% 36.18/36.59 [weight('<41,6,1,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.13.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(X1,X2)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_12]).
% 36.18/36.59 cnf('0.14.0.0',plain,
% 36.18/36.59 ( truth = big_V(truth,X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.13.2.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.14.1.0',plain,
% 36.18/36.59 ( truth = big_V(truth,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.14.0.0']),
% 36.18/36.59 [weight('<19,13,1,[1,0,0,0]>')]).
% 36.18/36.59 cnf('0.14.2.0',plain,
% 36.18/36.59 ( big_V(truth,X1) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_13]).
% 36.18/36.59 cnf('0.15.0.0',plain,
% 36.18/36.59 ( implies(X1,X1) = big_V(truth,X1) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.11.2.0'])).
% 36.18/36.59 cnf('0.15.0.1',plain,
% 36.18/36.59 ( implies(X1,X1) = truth ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.15.0.0','0.14.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.15.1.0',plain,
% 36.18/36.59 ( implies(X1,X1) = truth ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.15.0.1']),
% 36.18/36.59 [weight('<19,11,14,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.15.2.0',plain,
% 36.18/36.59 ( implies(X1,X1) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_14]).
% 36.18/36.59 cnf('0.16.0.0',plain,
% 36.18/36.59 ( big_V(X1,X1) = implies(truth,X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.15.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.16.0.1',plain,
% 36.18/36.59 ( big_V(X1,X1) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.16.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.16.1.0',plain,
% 36.18/36.59 ( big_V(X1,X1) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.16.0.1']),
% 36.18/36.59 [weight('<19,15,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.16.2.0',plain,
% 36.18/36.59 ( big_V(X1,X1) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_15]).
% 36.18/36.59 cnf('0.19.0.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.4.2.0'])).
% 36.18/36.59 cnf('0.19.0.1',plain,
% 36.18/36.59 ( big_V(X1,X2) = implies(implies(X2,X1),X1) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.19.0.0','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.19.0.2',plain,
% 36.18/36.59 ( big_V(X1,X2) = big_V(X2,X1) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.19.0.1','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.19.1.0',plain,
% 36.18/36.59 ( big_V(X1,X2) = big_V(X2,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.19.0.2']),
% 36.18/36.59 [weight('<48,4,5,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.19.2.0',plain,
% 36.18/36.59 ( big_V(X1,X2) = big_V(X2,X1) ),
% 36.18/36.59 inference(activate,[status(thm)],['0.19.1.0']),
% 36.18/36.59 [equation_2]).
% 36.18/36.59 cnf('0.20.0.0',plain,
% 36.18/36.59 ( big_V(X1,truth) = truth ),
% 36.18/36.59 inference(cp,[status(thm)],['0.19.2.0','0.14.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.20.1.0',plain,
% 36.18/36.59 ( big_V(X1,truth) = truth ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.20.0.0']),
% 36.18/36.59 [weight('<19,19,14,[1,0,0,0]>')]).
% 36.18/36.59 cnf('0.20.2.0',plain,
% 36.18/36.59 ( big_V(X1,truth) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_18]).
% 36.18/36.59 cnf('0.21.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,truth) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.13.2.0','0.20.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.21.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,truth) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.21.0.0']),
% 36.18/36.59 [weight('<19,20,13,[0,0,0,2]>')]).
% 36.18/36.59 cnf('0.21.2.0',plain,
% 36.18/36.59 ( implies(X1,truth) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_19]).
% 36.18/36.59 cnf('0.23.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.13.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.23.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.23.0.0']),
% 36.18/36.59 [weight('<41,19,13,[0,0,0,2]>')]).
% 36.18/36.59 cnf('0.23.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(X2,X1)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_21]).
% 36.18/36.59 cnf('0.25.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(implies(truth,X1),implies(X2,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.21.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.25.0.1',plain,
% 36.18/36.59 ( truth = implies(implies(truth,X1),implies(X2,X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.25.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.25.0.2',plain,
% 36.18/36.59 ( truth = implies(X1,implies(X2,X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.25.0.1','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.1','L')]).
% 36.18/36.59 cnf('0.25.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,implies(X2,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.25.0.2']),
% 36.18/36.59 [weight('<41,21,6,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.25.2.0',plain,
% 36.18/36.59 ( implies(X1,implies(X2,X1)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_23]).
% 36.18/36.59 cnf('0.27.0.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = not(not(X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.9.2.0','0.16.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.27.1.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = not(not(X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.27.0.0']),
% 36.18/36.59 [weight('<48,16,9,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.27.2.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = not(not(X1)) ),
% 36.18/36.59 inference(activate,[status(thm)],['0.27.1.0']),
% 36.18/36.59 [equation_3]).
% 36.18/36.59 cnf('0.28.0.0',plain,
% 36.18/36.59 ( big_hat(X1,X2) = not(big_V(not(X2),not(X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.9.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.28.0.1',plain,
% 36.18/36.59 ( big_hat(X1,X2) = big_hat(X2,X1) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.28.0.0','0.9.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.28.1.0',plain,
% 36.18/36.59 ( big_hat(X1,X2) = big_hat(X2,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.28.0.1']),
% 36.18/36.59 [weight('<48,19,9,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.28.2.0',plain,
% 36.18/36.59 ( big_hat(X1,X2) = big_hat(X2,X1) ),
% 36.18/36.59 inference(activate,[status(thm)],['0.28.1.0']),
% 36.18/36.59 [equation_4]).
% 36.18/36.59 cnf('0.29.0.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X1,X2)) = implies(truth,big_V(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.13.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.29.0.1',plain,
% 36.18/36.59 ( big_V(X1,big_V(X1,X2)) = big_V(X1,X2) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.29.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.29.1.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X1,X2)) = big_V(X1,X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.29.0.1']),
% 36.18/36.59 [weight('<53,13,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.29.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X1,X2)) = big_V(X1,X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_25]).
% 36.18/36.59 cnf('0.31.0.0',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,X1)) = implies(truth,implies(X2,X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.25.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.31.0.1',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,X1)) = implies(X2,X1) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.31.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.31.1.0',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,X1)) = implies(X2,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.31.0.1']),
% 36.18/36.59 [weight('<53,25,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.31.2.0',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,X1)) = implies(X2,X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_27]).
% 36.18/36.59 cnf('0.32.0.0',plain,
% 36.18/36.59 ( big_V(implies(X1,X2),X2) = implies(big_V(X1,X2),X2) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.32.1.0',plain,
% 36.18/36.59 ( big_V(implies(X1,X2),X2) = implies(big_V(X1,X2),X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.32.0.0']),
% 36.18/36.59 [weight('<65,5,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.32.1.1',plain,
% 36.18/36.59 ( big_V(X2,implies(X1,X2)) = implies(big_V(X1,X2),X2) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.32.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.32.1.2',plain,
% 36.18/36.59 ( implies(X1,X2) = implies(big_V(X1,X2),X2) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.32.1.1','0.31.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.32.2.0',plain,
% 36.18/36.59 ( implies(big_V(X1,X2),X2) = implies(X1,X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.32.1.2',theory(equality)]),
% 36.18/36.59 [x,rule_28]).
% 36.18/36.59 cnf('0.33.0.0',plain,
% 36.18/36.59 ( implies(X1,X2) = implies(big_V(X2,X1),X2) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.32.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.33.1.0',plain,
% 36.18/36.59 ( implies(X1,X2) = implies(big_V(X2,X1),X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.33.0.0']),
% 36.18/36.59 [weight('<53,32,19,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.33.2.0',plain,
% 36.18/36.59 ( implies(big_V(X1,X2),X1) = implies(X2,X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_29]).
% 36.18/36.59 cnf('0.34.0.0',plain,
% 36.18/36.59 ( truth = implies(implies(not(X1),not(truth)),X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.7.2.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.34.1.0',plain,
% 36.18/36.59 ( truth = implies(implies(not(X1),not(truth)),X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.34.0.0']),
% 36.18/36.59 [weight('<71,7,1,[1,0,0,6]>')]).
% 36.18/36.59 cnf('0.34.2.0',plain,
% 36.18/36.59 ( implies(implies(not(X1),not(truth)),X1) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_30]).
% 36.18/36.59 cnf('0.40.0.0',plain,
% 36.18/36.59 ( big_V(implies(not(X1),not(truth)),X1) = implies(truth,X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.34.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.40.0.1',plain,
% 36.18/36.59 ( big_V(implies(not(X1),not(truth)),X1) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.40.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.40.1.0',plain,
% 36.18/36.59 ( big_V(implies(not(X1),not(truth)),X1) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.40.0.1']),
% 36.18/36.59 [weight('<71,34,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.40.1.1',plain,
% 36.18/36.59 ( big_V(X1,implies(not(X1),not(truth))) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.40.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.40.2.0',plain,
% 36.18/36.59 ( big_V(X1,implies(not(X1),not(truth))) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.40.1.1',theory(equality)]),
% 36.18/36.59 [u,rule_36]).
% 36.18/36.59 cnf('0.42.0.0',plain,
% 36.18/36.59 ( big_hat(not(X1),X2) = not(big_V(big_hat(X1,X1),not(X2))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.9.2.0','0.27.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1.1','R')]).
% 36.18/36.59 cnf('0.42.1.0',plain,
% 36.18/36.59 ( big_hat(not(X1),X2) = not(big_V(big_hat(X1,X1),not(X2))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.42.0.0']),
% 36.18/36.59 [weight('<95,27,9,[0,1,0,2]>')]).
% 36.18/36.59 cnf('0.42.2.0',plain,
% 36.18/36.59 ( not(big_V(big_hat(X1,X1),not(X2))) = big_hat(not(X1),X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_38]).
% 36.18/36.59 cnf('0.43.0.0',plain,
% 36.18/36.59 ( big_hat(X1,not(X2)) = not(big_V(not(X1),big_hat(X2,X2))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.9.2.0','0.27.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1.2','R')]).
% 36.18/36.59 cnf('0.43.1.0',plain,
% 36.18/36.59 ( big_hat(X1,not(X2)) = not(big_V(not(X1),big_hat(X2,X2))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.43.0.0']),
% 36.18/36.59 [weight('<95,27,9,[0,1,0,4]>')]).
% 36.18/36.59 cnf('0.43.2.0',plain,
% 36.18/36.59 ( not(big_V(not(X1),big_hat(X2,X2))) = big_hat(X1,not(X2)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_39]).
% 36.18/36.59 cnf('0.46.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(implies(big_V(X1,X2),X3),implies(X1,X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.13.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.46.0.1',plain,
% 36.18/36.59 ( truth = implies(implies(big_V(X1,X2),X3),implies(X1,X3)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.46.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.46.1.0',plain,
% 36.18/36.59 ( truth = implies(implies(big_V(X1,X2),X3),implies(X1,X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.46.0.1']),
% 36.18/36.59 [weight('<109,13,6,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.46.2.0',plain,
% 36.18/36.59 ( implies(implies(big_V(X1,X2),X3),implies(X1,X3)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_42]).
% 36.18/36.59 cnf('0.47.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(X1,big_V(big_V(X1,X2),X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.46.2.0','0.13.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.47.0.1',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(big_V(X1,X2),X3)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.47.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.47.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(big_V(X1,X2),X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.47.0.1']),
% 36.18/36.59 [weight('<71,46,13,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.47.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(big_V(X1,X2),X3)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_43]).
% 36.18/36.59 cnf('0.48.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(X1,big_V(X2,big_V(X1,X3)))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.46.2.0','0.23.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.48.0.1',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,big_V(X1,X3))) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.48.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.48.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,big_V(X1,X3))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.48.0.1']),
% 36.18/36.59 [weight('<71,46,23,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.48.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(X2,big_V(X1,X3))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_44]).
% 36.18/36.59 cnf('0.49.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(X1,implies(X2,big_V(X1,X3)))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.46.2.0','0.25.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.49.0.1',plain,
% 36.18/36.59 ( truth = implies(X1,implies(X2,big_V(X1,X3))) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.49.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.49.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,implies(X2,big_V(X1,X3))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.49.0.1']),
% 36.18/36.59 [weight('<71,46,25,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.49.2.0',plain,
% 36.18/36.59 ( implies(X1,implies(X2,big_V(X1,X3))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_45]).
% 36.18/36.59 cnf('0.51.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(big_V(X2,X1),X3)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.47.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.1','L')]).
% 36.18/36.59 cnf('0.51.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(big_V(X2,X1),X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.51.0.0']),
% 36.18/36.59 [weight('<71,47,19,[1,0,0,3]>')]).
% 36.18/36.59 cnf('0.51.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(big_V(X2,X1),X3)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_47]).
% 36.18/36.59 cnf('0.54.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.48.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.2','L')]).
% 36.18/36.59 cnf('0.54.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.54.0.0']),
% 36.18/36.59 [weight('<71,48,19,[1,0,0,4]>')]).
% 36.18/36.59 cnf('0.54.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(X2,big_V(X3,X1))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_50]).
% 36.18/36.59 cnf('0.55.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,implies(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.48.2.0','0.31.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.2','L')]).
% 36.18/36.59 cnf('0.55.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,big_V(X2,implies(X3,X1))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.55.0.0']),
% 36.18/36.59 [weight('<71,48,31,[1,0,0,4]>')]).
% 36.18/36.59 cnf('0.55.2.0',plain,
% 36.18/36.59 ( implies(X1,big_V(X2,implies(X3,X1))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_51]).
% 36.18/36.59 cnf('0.56.0.0',plain,
% 36.18/36.59 ( truth = implies(not(truth),X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.55.2.0','0.40.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.56.1.0',plain,
% 36.18/36.59 ( truth = implies(not(truth),X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.56.0.0']),
% 36.18/36.59 [weight('<29,55,40,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.56.2.0',plain,
% 36.18/36.59 ( implies(not(truth),X1) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_52]).
% 36.18/36.59 cnf('0.57.0.0',plain,
% 36.18/36.59 ( big_V(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = implies(truth,implies(implies(X2,X3),implies(X1,X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.6.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.57.0.1',plain,
% 36.18/36.59 ( big_V(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = implies(implies(X2,X3),implies(X1,X3)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.57.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.57.1.0',plain,
% 36.18/36.59 ( big_V(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = implies(implies(X2,X3),implies(X1,X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.57.0.1']),
% 36.18/36.59 [weight('<?,6,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.57.2.0',plain,
% 36.18/36.59 ( big_V(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = implies(implies(X2,X3),implies(X1,X3)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_53]).
% 36.18/36.59 cnf('0.59.0.0',plain,
% 36.18/36.59 ( big_V(not(truth),X1) = implies(truth,X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.56.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.59.0.1',plain,
% 36.18/36.59 ( big_V(not(truth),X1) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.59.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.59.1.0',plain,
% 36.18/36.59 ( big_V(not(truth),X1) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.59.0.1']),
% 36.18/36.59 [weight('<29,56,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.59.2.0',plain,
% 36.18/36.59 ( big_V(not(truth),X1) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_55]).
% 36.18/36.59 cnf('0.60.0.0',plain,
% 36.18/36.59 ( big_hat(truth,X1) = not(not(X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.9.2.0','0.59.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.60.1.0',plain,
% 36.18/36.59 ( big_hat(truth,X1) = not(not(X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.60.0.0']),
% 36.18/36.59 [weight('<27,59,9,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.60.2.0',plain,
% 36.18/36.59 ( not(not(X1)) = big_hat(truth,X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_56]).
% 36.18/36.59 cnf('0.62.0.0',plain,
% 36.18/36.59 ( X1 = big_V(X1,not(truth)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.59.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.62.1.0',plain,
% 36.18/36.59 ( X1 = big_V(X1,not(truth)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.62.0.0']),
% 36.18/36.59 [weight('<29,59,19,[1,0,0,0]>')]).
% 36.18/36.59 cnf('0.62.2.0',plain,
% 36.18/36.59 ( big_V(X1,not(truth)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_58]).
% 36.18/36.59 cnf('0.68.0.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = not(not(X1)) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.27.2.0'])).
% 36.18/36.59 cnf('0.68.0.1',plain,
% 36.18/36.59 ( big_hat(X1,X1) = big_hat(truth,X1) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.68.0.0','0.60.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.68.1.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = big_hat(truth,X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.68.0.1']),
% 36.18/36.59 [weight('<48,27,60,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.68.2.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = big_hat(truth,X1) ),
% 36.18/36.59 inference(activate,[status(thm)],['0.68.1.0']),
% 36.18/36.59 [equation_5]).
% 36.18/36.59 cnf('0.71.0.0',plain,
% 36.18/36.59 ( truth = implies(X1,implies(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.49.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.2','L')]).
% 36.18/36.59 cnf('0.71.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,implies(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.71.0.0']),
% 36.18/36.59 [weight('<71,49,19,[1,0,0,4]>')]).
% 36.18/36.59 cnf('0.71.2.0',plain,
% 36.18/36.59 ( implies(X1,implies(X2,big_V(X3,X1))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_65]).
% 36.18/36.59 cnf('0.85.0.0',plain,
% 36.18/36.59 ( big_hat(truth,big_V(not(X1),not(X2))) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.60.2.0','0.9.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.85.1.0',plain,
% 36.18/36.59 ( big_hat(truth,big_V(not(X1),not(X2))) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.85.0.0']),
% 36.18/36.59 [weight('<95,60,9,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.85.2.0',plain,
% 36.18/36.59 ( big_hat(truth,big_V(not(X1),not(X2))) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.85.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_79]).
% 36.18/36.59 cnf('0.88.0.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X1,X2),X3)) = implies(truth,big_V(big_V(X1,X2),X3)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.47.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.88.0.1',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X1,X2),X3)) = big_V(big_V(X1,X2),X3) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.88.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.88.1.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X1,X2),X3)) = big_V(big_V(X1,X2),X3) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.88.0.1']),
% 36.18/36.59 [weight('<103,47,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.88.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X1,X2),X3)) = big_V(big_V(X1,X2),X3) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.88.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_82]).
% 36.18/36.59 cnf('0.89.0.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X1,X3))) = implies(truth,big_V(X2,big_V(X1,X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.48.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.89.0.1',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X1,X3))) = big_V(X2,big_V(X1,X3)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.89.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.89.1.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X1,X3))) = big_V(X2,big_V(X1,X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.89.0.1']),
% 36.18/36.59 [weight('<103,48,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.89.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X1,X3))) = big_V(X2,big_V(X1,X3)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.89.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_83]).
% 36.18/36.59 cnf('0.91.0.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X2,X1),X3)) = implies(truth,big_V(big_V(X2,X1),X3)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.51.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.91.0.1',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X2,X1),X3)) = big_V(big_V(X2,X1),X3) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.91.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.91.1.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X2,X1),X3)) = big_V(big_V(X2,X1),X3) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.91.0.1']),
% 36.18/36.59 [weight('<103,51,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.91.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(big_V(X2,X1),X3)) = big_V(big_V(X2,X1),X3) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.91.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_85]).
% 36.18/36.59 cnf('0.93.0.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X3,X1))) = implies(truth,big_V(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.54.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.93.0.1',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X3,X1))) = big_V(X2,big_V(X3,X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.93.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.93.1.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X3,X1))) = big_V(X2,big_V(X3,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.93.0.1']),
% 36.18/36.59 [weight('<103,54,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.93.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_V(X2,big_V(X3,X1))) = big_V(X2,big_V(X3,X1)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.93.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_87]).
% 36.18/36.59 cnf('0.95.0.0',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,big_V(X3,X1))) = implies(truth,implies(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.71.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.95.0.1',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,big_V(X3,X1))) = implies(X2,big_V(X3,X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.95.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.95.1.0',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,big_V(X3,X1))) = implies(X2,big_V(X3,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.95.0.1']),
% 36.18/36.59 [weight('<103,71,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.95.2.0',plain,
% 36.18/36.59 ( big_V(X1,implies(X2,big_V(X3,X1))) = implies(X2,big_V(X3,X1)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_89]).
% 36.18/36.59 cnf('0.100.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(implies(big_V(X1,X2),X3),implies(X2,X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.23.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.100.0.1',plain,
% 36.18/36.59 ( truth = implies(implies(big_V(X1,X2),X3),implies(X2,X3)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.100.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.100.1.0',plain,
% 36.18/36.59 ( truth = implies(implies(big_V(X1,X2),X3),implies(X2,X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.100.0.1']),
% 36.18/36.59 [weight('<109,23,6,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.100.2.0',plain,
% 36.18/36.59 ( implies(implies(big_V(X1,X2),X3),implies(X2,X3)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.100.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_94]).
% 36.18/36.59 cnf('0.101.0.0',plain,
% 36.18/36.59 ( truth = implies(implies(X1,X2),implies(truth,implies(X1,big_V(X3,X2)))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.23.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.1','L')]).
% 36.18/36.59 cnf('0.101.0.1',plain,
% 36.18/36.59 ( truth = implies(implies(X1,X2),implies(X1,big_V(X3,X2))) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.101.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.2','L')]).
% 36.18/36.59 cnf('0.101.1.0',plain,
% 36.18/36.59 ( truth = implies(implies(X1,X2),implies(X1,big_V(X3,X2))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.101.0.1']),
% 36.18/36.59 [weight('<109,23,6,[0,0,0,5]>')]).
% 36.18/36.59 cnf('0.101.2.0',plain,
% 36.18/36.59 ( implies(implies(X1,X2),implies(X1,big_V(X3,X2))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.101.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_95]).
% 36.18/36.59 cnf('0.102.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(implies(implies(X1,X2),X3),implies(X2,X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.25.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.102.0.1',plain,
% 36.18/36.59 ( truth = implies(implies(implies(X1,X2),X3),implies(X2,X3)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.102.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.102.1.0',plain,
% 36.18/36.59 ( truth = implies(implies(implies(X1,X2),X3),implies(X2,X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.102.0.1']),
% 36.18/36.59 [weight('<109,25,6,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.102.2.0',plain,
% 36.18/36.59 ( implies(implies(implies(X1,X2),X3),implies(X2,X3)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_96]).
% 36.18/36.59 cnf('0.103.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(not(X1),implies(X1,X2))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.102.2.0','0.7.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.103.0.1',plain,
% 36.18/36.59 ( truth = implies(not(X1),implies(X1,X2)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.103.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.103.1.0',plain,
% 36.18/36.59 ( truth = implies(not(X1),implies(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.103.0.1']),
% 36.18/36.59 [weight('<55,102,7,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.103.2.0',plain,
% 36.18/36.59 ( implies(not(X1),implies(X1,X2)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.103.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_97]).
% 36.18/36.59 cnf('0.105.0.0',plain,
% 36.18/36.59 ( big_V(not(X1),implies(X1,X2)) = implies(truth,implies(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.103.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.105.0.1',plain,
% 36.18/36.59 ( big_V(not(X1),implies(X1,X2)) = implies(X1,X2) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.105.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.105.1.0',plain,
% 36.18/36.59 ( big_V(not(X1),implies(X1,X2)) = implies(X1,X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.105.0.1']),
% 36.18/36.59 [weight('<69,103,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.105.2.0',plain,
% 36.18/36.59 ( big_V(not(X1),implies(X1,X2)) = implies(X1,X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.105.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_99]).
% 36.18/36.59 cnf('0.106.0.0',plain,
% 36.18/36.59 ( truth = implies(not(implies(X1,X2)),big_V(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.103.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.106.1.0',plain,
% 36.18/36.59 ( truth = implies(not(implies(X1,X2)),big_V(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.106.0.0']),
% 36.18/36.59 [weight('<89,103,5,[1,0,0,3]>')]).
% 36.18/36.59 cnf('0.106.2.0',plain,
% 36.18/36.59 ( implies(not(implies(X1,X2)),big_V(X1,X2)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_100]).
% 36.18/36.59 cnf('0.107.0.0',plain,
% 36.18/36.59 ( truth = implies(not(implies(X1,not(truth))),X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.106.2.0','0.62.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.107.1.0',plain,
% 36.18/36.59 ( truth = implies(not(implies(X1,not(truth))),X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.107.0.0']),
% 36.18/36.59 [weight('<71,106,62,[1,0,0,5]>')]).
% 36.18/36.59 cnf('0.107.2.0',plain,
% 36.18/36.59 ( implies(not(implies(X1,not(truth))),X1) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_101]).
% 36.18/36.59 cnf('0.108.0.0',plain,
% 36.18/36.59 ( truth = implies(big_V(X1,X2),implies(implies(X2,X3),implies(implies(X1,X2),X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.108.1.0',plain,
% 36.18/36.59 ( truth = implies(big_V(X1,X2),implies(implies(X2,X3),implies(implies(X1,X2),X3))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.108.0.0']),
% 36.18/36.59 [weight('<?,6,5,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.108.2.0',plain,
% 36.18/36.59 ( implies(big_V(X1,X2),implies(implies(X2,X3),implies(implies(X1,X2),X3))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_102]).
% 36.18/36.59 cnf('0.110.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(X1,implies(not(X1),not(truth)))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.7.2.0','0.107.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.110.0.1',plain,
% 36.18/36.59 ( truth = implies(X1,implies(not(X1),not(truth))) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.110.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.110.1.0',plain,
% 36.18/36.59 ( truth = implies(X1,implies(not(X1),not(truth))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.110.0.1']),
% 36.18/36.59 [weight('<71,107,7,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.110.2.0',plain,
% 36.18/36.59 ( implies(X1,implies(not(X1),not(truth))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.110.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_104]).
% 36.18/36.59 cnf('0.111.0.0',plain,
% 36.18/36.59 ( big_V(X1,implies(not(X1),not(truth))) = implies(truth,implies(not(X1),not(truth))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.110.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.111.0.1',plain,
% 36.18/36.59 ( X1 = implies(truth,implies(not(X1),not(truth))) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.111.0.0','0.40.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.111.0.2',plain,
% 36.18/36.59 ( X1 = implies(not(X1),not(truth)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.111.0.1','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.111.1.0',plain,
% 36.18/36.59 ( X1 = implies(not(X1),not(truth)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.111.0.2']),
% 36.18/36.59 [weight('<41,110,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.111.2.0',plain,
% 36.18/36.59 ( implies(not(X1),not(truth)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.111.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_105]).
% 36.18/36.59 cnf('0.112.0.0',plain,
% 36.18/36.59 ( big_V(not(X1),not(truth)) = implies(X1,not(truth)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.111.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.112.0.1',plain,
% 36.18/36.59 ( not(X1) = implies(X1,not(truth)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.112.0.0','0.62.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.112.1.0',plain,
% 36.18/36.59 ( not(X1) = implies(X1,not(truth)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.112.0.1']),
% 36.18/36.59 [weight('<34,111,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.112.2.0',plain,
% 36.18/36.59 ( implies(X1,not(truth)) = not(X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.112.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_106]).
% 36.18/36.59 cnf('0.113.0.0',plain,
% 36.18/36.59 ( implies(not(X1),not(truth)) = X1 ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.111.2.0'])).
% 36.18/36.59 cnf('0.113.0.1',plain,
% 36.18/36.59 ( not(not(X1)) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.113.0.0','0.112.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.113.0.2',plain,
% 36.18/36.59 ( big_hat(truth,X1) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.113.0.1','0.60.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.113.1.0',plain,
% 36.18/36.59 ( big_hat(truth,X1) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.113.0.2']),
% 36.18/36.59 [weight('<19,111,112,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.113.2.0',plain,
% 36.18/36.59 ( big_hat(truth,X1) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.113.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_107]).
% 36.18/36.59 cnf('0.114.0.0',plain,
% 36.18/36.59 ( not(not(X1)) = big_hat(truth,X1) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.60.2.0'])).
% 36.18/36.59 cnf('0.114.0.1',plain,
% 36.18/36.59 ( not(not(X1)) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.114.0.0','0.113.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.114.1.0',plain,
% 36.18/36.59 ( not(not(X1)) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.114.0.1']),
% 36.18/36.59 [weight('<19,60,113,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.114.2.0',plain,
% 36.18/36.59 ( not(not(X1)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.114.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_108]).
% 36.18/36.59 cnf('0.115.0.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = big_hat(truth,X1) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.68.2.0'])).
% 36.18/36.59 cnf('0.115.0.1',plain,
% 36.18/36.59 ( big_hat(X1,X1) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.115.0.0','0.113.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.115.1.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.115.0.1']),
% 36.18/36.59 [weight('<19,68,113,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.115.2.0',plain,
% 36.18/36.59 ( big_hat(X1,X1) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.115.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_109]).
% 36.18/36.59 cnf('0.119.0.0',plain,
% 36.18/36.59 ( not(big_V(big_hat(X1,X1),not(X2))) = big_hat(not(X1),X2) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.42.2.0'])).
% 36.18/36.59 cnf('0.119.0.1',plain,
% 36.18/36.59 ( not(big_V(X1,not(X2))) = big_hat(not(X1),X2) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.119.0.0','0.115.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1.1','L')]).
% 36.18/36.59 cnf('0.119.1.0',plain,
% 36.18/36.59 ( not(big_V(X1,not(X2))) = big_hat(not(X1),X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.119.0.1']),
% 36.18/36.59 [weight('<59,42,115,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.119.2.0',plain,
% 36.18/36.59 ( not(big_V(X1,not(X2))) = big_hat(not(X1),X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.119.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_113]).
% 36.18/36.59 cnf('0.120.0.0',plain,
% 36.18/36.59 ( not(big_V(not(X1),big_hat(X2,X2))) = big_hat(X1,not(X2)) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.43.2.0'])).
% 36.18/36.59 cnf('0.120.0.1',plain,
% 36.18/36.59 ( not(big_V(not(X1),X2)) = big_hat(X1,not(X2)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.120.0.0','0.115.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1.2','L')]).
% 36.18/36.59 cnf('0.120.1.0',plain,
% 36.18/36.59 ( not(big_V(not(X1),X2)) = big_hat(X1,not(X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.120.0.1']),
% 36.18/36.59 [weight('<59,43,115,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.120.2.0',plain,
% 36.18/36.59 ( not(big_V(not(X1),X2)) = big_hat(X1,not(X2)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.120.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_114]).
% 36.18/36.59 cnf('0.121.0.0',plain,
% 36.18/36.59 ( big_hat(truth,big_V(not(X1),not(X2))) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(interreduction_right,[status(thm)],['0.85.2.0'])).
% 36.18/36.59 cnf('0.121.0.1',plain,
% 36.18/36.59 ( big_V(not(X1),not(X2)) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.121.0.0','0.113.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.121.1.0',plain,
% 36.18/36.59 ( big_V(not(X1),not(X2)) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.121.0.1']),
% 36.18/36.59 [weight('<59,85,113,[0,0,0,0]>')]).
% 36.18/36.59 cnf('0.121.2.0',plain,
% 36.18/36.59 ( big_V(not(X1),not(X2)) = not(big_hat(X1,X2)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.121.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_115]).
% 36.18/36.59 cnf('0.122.0.0',plain,
% 36.18/36.59 ( big_V(X1,not(X2)) = not(big_hat(not(X1),X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.114.2.0','0.119.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.122.1.0',plain,
% 36.18/36.59 ( big_V(X1,not(X2)) = not(big_hat(not(X1),X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.122.0.0']),
% 36.18/36.59 [weight('<59,119,114,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.122.2.0',plain,
% 36.18/36.59 ( not(big_hat(not(X1),X2)) = big_V(X1,not(X2)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.122.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_116]).
% 36.18/36.59 cnf('0.123.0.0',plain,
% 36.18/36.59 ( big_hat(not(X1),not(X2)) = not(big_V(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.119.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1.2','L')]).
% 36.18/36.59 cnf('0.123.1.0',plain,
% 36.18/36.59 ( big_hat(not(X1),not(X2)) = not(big_V(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.123.0.0']),
% 36.18/36.59 [weight('<59,119,114,[1,0,0,3]>')]).
% 36.18/36.59 cnf('0.123.2.0',plain,
% 36.18/36.59 ( big_hat(not(X1),not(X2)) = not(big_V(X1,X2)) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.123.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_117]).
% 36.18/36.59 cnf('0.124.0.0',plain,
% 36.18/36.59 ( big_V(not(X1),X2) = not(big_hat(X1,not(X2))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.114.2.0','0.120.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.124.1.0',plain,
% 36.18/36.59 ( big_V(not(X1),X2) = not(big_hat(X1,not(X2))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.124.0.0']),
% 36.18/36.59 [weight('<59,120,114,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.124.2.0',plain,
% 36.18/36.59 ( not(big_hat(X1,not(X2))) = big_V(not(X1),X2) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_118]).
% 36.18/36.59 cnf('0.125.0.0',plain,
% 36.18/36.59 ( truth = implies(not(big_V(X1,X2)),implies(X1,not(truth))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.46.2.0','0.112.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.125.0.1',plain,
% 36.18/36.59 ( truth = implies(not(big_V(X1,X2)),not(X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.125.0.0','0.112.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.2','L')]).
% 36.18/36.59 cnf('0.125.1.0',plain,
% 36.18/36.59 ( truth = implies(not(big_V(X1,X2)),not(X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.125.0.1']),
% 36.18/36.59 [weight('<71,112,46,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.125.2.0',plain,
% 36.18/36.59 ( implies(not(big_V(X1,X2)),not(X1)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_119]).
% 36.18/36.59 cnf('0.126.0.0',plain,
% 36.18/36.59 ( truth = implies(not(not(big_hat(X1,X2))),not(not(X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.125.2.0','0.121.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1.1','L')]).
% 36.18/36.59 cnf('0.126.0.1',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),not(not(X1))) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.126.0.0','0.114.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.1','L')]).
% 36.18/36.59 cnf('0.126.0.2',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),X1) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.126.0.1','0.114.2.0',theory(equality)]),
% 36.18/36.59 [pos('R.2','L')]).
% 36.18/36.59 cnf('0.126.1.0',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),X1) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.126.0.2']),
% 36.18/36.59 [weight('<41,125,121,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.126.2.0',plain,
% 36.18/36.59 ( implies(big_hat(X1,X2),X1) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.126.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_120]).
% 36.18/36.59 cnf('0.127.0.0',plain,
% 36.18/36.59 ( big_V(big_hat(X1,X2),X1) = implies(truth,X1) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.126.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.127.0.1',plain,
% 36.18/36.59 ( big_V(big_hat(X1,X2),X1) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.127.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.127.1.0',plain,
% 36.18/36.59 ( big_V(big_hat(X1,X2),X1) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.127.0.1']),
% 36.18/36.59 [weight('<41,126,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.127.1.1',plain,
% 36.18/36.59 ( big_V(X1,big_hat(X1,X2)) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.127.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.127.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_hat(X1,X2)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.127.1.1',theory(equality)]),
% 36.18/36.59 [u,rule_121]).
% 36.18/36.59 cnf('0.129.0.0',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),X2) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.126.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.129.1.0',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.129.0.0']),
% 36.18/36.59 [weight('<41,126,28,[1,0,0,1]>')]).
% 36.18/36.59 cnf('0.129.2.0',plain,
% 36.18/36.59 ( implies(big_hat(X1,X2),X2) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.129.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_123]).
% 36.18/36.59 cnf('0.130.0.0',plain,
% 36.18/36.59 ( X1 = big_V(X1,big_hat(X2,X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.127.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.130.1.0',plain,
% 36.18/36.59 ( X1 = big_V(X1,big_hat(X2,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.130.0.0']),
% 36.18/36.59 [weight('<41,127,28,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.130.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_hat(X2,X1)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.130.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_124]).
% 36.18/36.59 cnf('0.133.0.0',plain,
% 36.18/36.59 ( big_hat(X1,not(big_hat(not(X1),X2))) = not(not(X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.120.2.0','0.127.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.133.0.1',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X1,not(X2))) = not(not(X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.133.0.0','0.122.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.133.0.2',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X1,not(X2))) = X1 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.133.0.1','0.114.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.133.1.0',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X1,not(X2))) = X1 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.133.0.2']),
% 36.18/36.59 [weight('<55,127,120,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.133.2.0',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X1,not(X2))) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 36.18/36.59 [u,rule_127]).
% 36.18/36.59 cnf('0.134.0.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.133.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.2','L')]).
% 36.18/36.59 cnf('0.134.1.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.134.0.0']),
% 36.18/36.59 [weight('<41,133,114,[1,0,0,4]>')]).
% 36.18/36.59 cnf('0.134.2.0',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X1,X2)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_128]).
% 36.18/36.59 cnf('0.135.0.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(X2,X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.134.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.135.1.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(X2,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.135.0.0']),
% 36.18/36.59 [weight('<41,134,19,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.135.2.0',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X2,X1)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.135.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_129]).
% 36.18/36.59 cnf('0.136.0.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,implies(X2,X1)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.134.2.0','0.31.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.136.1.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,implies(X2,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.136.0.0']),
% 36.18/36.59 [weight('<41,134,31,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.136.2.0',plain,
% 36.18/36.59 ( big_hat(X1,implies(X2,X1)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.136.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_130]).
% 36.18/36.59 cnf('0.138.0.0',plain,
% 36.18/36.59 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),X2) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.135.2.0','0.130.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.138.1.0',plain,
% 36.18/36.59 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.138.0.0']),
% 36.18/36.59 [weight('<53,135,130,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.138.1.1',plain,
% 36.18/36.59 ( big_hat(X1,X2) = big_hat(X2,big_hat(X1,X2)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.138.1.0','0.28.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.138.2.0',plain,
% 36.18/36.59 ( big_hat(X1,big_hat(X2,X1)) = big_hat(X2,X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.138.1.1',theory(equality)]),
% 36.18/36.59 [x,rule_132]).
% 36.18/36.59 cnf('0.142.0.0',plain,
% 36.18/36.59 ( not(X1) = big_hat(not(X1),implies(X1,X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.134.2.0','0.105.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.142.1.0',plain,
% 36.18/36.59 ( not(X1) = big_hat(not(X1),implies(X1,X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.142.0.0']),
% 36.18/36.59 [weight('<62,134,105,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.142.2.0',plain,
% 36.18/36.59 ( big_hat(not(X1),implies(X1,X2)) = not(X1) ),
% 36.18/36.59 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_136]).
% 36.18/36.59 cnf('0.151.0.0',plain,
% 36.18/36.59 ( truth = implies(truth,implies(big_hat(X1,X2),big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.101.2.0','0.126.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.151.0.1',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),big_V(X3,X1)) ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.151.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.151.1.0',plain,
% 36.18/36.59 ( truth = implies(big_hat(X1,X2),big_V(X3,X1)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.151.0.1']),
% 36.18/36.59 [weight('<71,126,101,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.151.2.0',plain,
% 36.18/36.59 ( implies(big_hat(X1,X2),big_V(X3,X1)) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.151.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_145]).
% 36.18/36.59 cnf('0.159.0.0',plain,
% 36.18/36.59 ( truth = implies(implies(X1,implies(X2,X3)),implies(big_V(X2,X3),implies(X1,X3))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.6.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2.1','L')]).
% 36.18/36.59 cnf('0.159.1.0',plain,
% 36.18/36.59 ( truth = implies(implies(X1,implies(X2,X3)),implies(big_V(X2,X3),implies(X1,X3))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.159.0.0']),
% 36.18/36.59 [weight('<?,6,5,[1,0,0,5]>')]).
% 36.18/36.59 cnf('0.159.2.0',plain,
% 36.18/36.59 ( implies(implies(X1,implies(X2,X3)),implies(big_V(X2,X3),implies(X1,X3))) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.159.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_153]).
% 36.18/36.59 cnf('0.167.0.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(big_V(X2,X1),X3)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.134.2.0','0.91.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.167.1.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(big_V(X2,X1),X3)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.167.0.0']),
% 36.18/36.59 [weight('<71,134,91,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.167.2.0',plain,
% 36.18/36.59 ( big_hat(X1,big_V(big_V(X2,X1),X3)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.167.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_161]).
% 36.18/36.59 cnf('0.169.0.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.134.2.0','0.93.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.169.1.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,big_V(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.169.0.0']),
% 36.18/36.59 [weight('<71,134,93,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.169.2.0',plain,
% 36.18/36.59 ( big_hat(X1,big_V(X2,big_V(X3,X1))) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.169.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_163]).
% 36.18/36.59 cnf('0.171.0.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,implies(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.134.2.0','0.95.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.171.1.0',plain,
% 36.18/36.59 ( X1 = big_hat(X1,implies(X2,big_V(X3,X1))) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.171.0.0']),
% 36.18/36.59 [weight('<71,134,95,[1,0,0,2]>')]).
% 36.18/36.59 cnf('0.171.2.0',plain,
% 36.18/36.59 ( big_hat(X1,implies(X2,big_V(X3,X1))) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.171.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_165]).
% 36.18/36.59 cnf('0.177.0.0',plain,
% 36.18/36.59 ( truth = implies(big_hat(big_hat(X1,X2),X3),X2) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.151.2.0','0.130.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.2','L')]).
% 36.18/36.59 cnf('0.177.1.0',plain,
% 36.18/36.59 ( truth = implies(big_hat(big_hat(X1,X2),X3),X2) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.177.0.0']),
% 36.18/36.59 [weight('<71,151,130,[1,0,0,4]>')]).
% 36.18/36.59 cnf('0.177.2.0',plain,
% 36.18/36.59 ( implies(big_hat(big_hat(X1,X2),X3),X2) = truth ),
% 36.18/36.59 inference(orient,[status(thm)],['0.177.1.0',theory(equality)]),
% 36.18/36.59 [x,rule_171]).
% 36.18/36.59 cnf('0.186.0.0',plain,
% 36.18/36.59 ( big_V(big_hat(big_hat(X1,X2),X3),X2) = implies(truth,X2) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.5.2.0','0.177.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.186.0.1',plain,
% 36.18/36.59 ( big_V(big_hat(big_hat(X1,X2),X3),X2) = X2 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.186.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.59 [pos('R','L')]).
% 36.18/36.59 cnf('0.186.1.0',plain,
% 36.18/36.59 ( big_V(big_hat(big_hat(X1,X2),X3),X2) = X2 ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.186.0.1']),
% 36.18/36.59 [weight('<71,177,5,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.186.1.1',plain,
% 36.18/36.59 ( big_V(X2,big_hat(big_hat(X1,X2),X3)) = X2 ),
% 36.18/36.59 inference(reduction,[status(thm)],['0.186.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.59 [pos('L','L')]).
% 36.18/36.59 cnf('0.186.2.0',plain,
% 36.18/36.59 ( big_V(X1,big_hat(big_hat(X2,X1),X3)) = X1 ),
% 36.18/36.59 inference(orient,[status(thm)],['0.186.1.1',theory(equality)]),
% 36.18/36.59 [u,rule_180]).
% 36.18/36.59 cnf('0.189.0.0',plain,
% 36.18/36.59 ( implies(not(X1),X2) = big_V(X1,implies(not(X1),X2)) ),
% 36.18/36.59 inference(cp,[status(thm)],['0.105.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.59 [pos('L.1','L')]).
% 36.18/36.59 cnf('0.189.1.0',plain,
% 36.18/36.59 ( implies(not(X1),X2) = big_V(X1,implies(not(X1),X2)) ),
% 36.18/36.59 inference(weigh,[status(thm)],['0.189.0.0']),
% 36.18/36.59 [weight('<76,114,105,[0,0,0,1]>')]).
% 36.18/36.59 cnf('0.189.2.0',plain,
% 36.18/36.59 ( big_V(X1,implies(not(X1),X2)) = implies(not(X1),X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.189.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_183]).
% 36.18/36.60 cnf('0.197.0.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_V(X1,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.167.2.0','0.127.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.197.1.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_V(X1,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.197.0.0']),
% 36.18/36.60 [weight('<87,167,127,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.197.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),big_V(X1,X3)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.197.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_191]).
% 36.18/36.60 cnf('0.198.0.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_V(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.167.2.0','0.130.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.198.1.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_V(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.198.0.0']),
% 36.18/36.60 [weight('<87,167,130,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.198.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),big_V(X2,X3)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.198.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_192]).
% 36.18/36.60 cnf('0.199.0.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_V(X3,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.169.2.0','0.127.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.199.1.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_V(X3,X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.199.0.0']),
% 36.18/36.60 [weight('<87,169,127,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.199.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),big_V(X3,X1)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.199.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_193]).
% 36.18/36.60 cnf('0.201.0.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),implies(X3,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.171.2.0','0.127.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.201.1.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),implies(X3,X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.201.0.0']),
% 36.18/36.60 [weight('<87,171,127,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.201.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),implies(X3,X1)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.201.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_195]).
% 36.18/36.60 cnf('0.204.0.0',plain,
% 36.18/36.60 ( big_V(X1,X2) = big_V(big_V(X1,X2),big_hat(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.186.2.0','0.135.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.204.1.0',plain,
% 36.18/36.60 ( big_V(X1,X2) = big_V(big_V(X1,X2),big_hat(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.204.0.0']),
% 36.18/36.60 [weight('<87,186,135,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.204.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_hat(X2,X3)) = big_V(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.204.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_198]).
% 36.18/36.60 cnf('0.210.0.0',plain,
% 36.18/36.60 ( truth = implies(implies(implies(X1,X2),X3),implies(implies(X3,X2),big_V(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.6.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.210.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(implies(X1,X2),X3),implies(implies(X3,X2),big_V(X1,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.210.0.0']),
% 36.18/36.60 [weight('<?,6,5,[1,0,0,8]>')]).
% 36.18/36.60 cnf('0.210.2.0',plain,
% 36.18/36.60 ( implies(implies(implies(X1,X2),X3),implies(implies(X3,X2),big_V(X1,X2))) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.210.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_204]).
% 36.18/36.60 cnf('0.313.0.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(not(big_hat(X1,X2)),not(X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.32.2.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.313.1.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(not(big_hat(X1,X2)),not(X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.313.0.0']),
% 36.18/36.60 [weight('<103,121,32,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.313.2.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),not(X2)) = implies(not(X1),not(X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.313.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_307]).
% 36.18/36.60 cnf('0.314.0.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(not(big_hat(X2,X1)),not(X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.33.2.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.314.1.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(not(big_hat(X2,X1)),not(X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.314.0.0']),
% 36.18/36.60 [weight('<103,121,33,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.314.2.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),not(X1)) = implies(not(X2),not(X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.314.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_308]).
% 36.18/36.60 cnf('0.363.0.0',plain,
% 36.18/36.60 ( big_V(implies(not(X1),not(X2)),implies(X2,X1)) = implies(truth,implies(X2,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.7.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.363.0.1',plain,
% 36.18/36.60 ( big_V(implies(not(X1),not(X2)),implies(X2,X1)) = implies(X2,X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.363.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.363.1.0',plain,
% 36.18/36.60 ( big_V(implies(not(X1),not(X2)),implies(X2,X1)) = implies(X2,X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.363.0.1']),
% 36.18/36.60 [weight('<?,7,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.363.1.1',plain,
% 36.18/36.60 ( big_V(implies(X2,X1),implies(not(X1),not(X2))) = implies(X2,X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.363.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.363.2.0',plain,
% 36.18/36.60 ( big_V(implies(X1,X2),implies(not(X2),not(X1))) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.363.1.1',theory(equality)]),
% 36.18/36.60 [u,rule_357]).
% 36.18/36.60 cnf('0.408.0.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(not(X2),implies(X1,not(truth)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.6.2.0','0.112.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.408.0.1',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(not(X2),not(X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.408.0.0','0.112.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2.2','L')]).
% 36.18/36.60 cnf('0.408.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(not(X2),not(X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.408.0.1']),
% 36.18/36.60 [weight('<109,112,6,[0,0,0,5]>')]).
% 36.18/36.60 cnf('0.408.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(not(X2),not(X1))) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.408.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_402]).
% 36.18/36.60 cnf('0.409.0.0',plain,
% 36.18/36.60 ( big_V(implies(X1,X2),implies(not(X2),not(X1))) = implies(truth,implies(not(X2),not(X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.408.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.409.0.1',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(truth,implies(not(X2),not(X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.409.0.0','0.363.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.409.0.2',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(not(X2),not(X1)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.409.0.1','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.409.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(not(X2),not(X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.409.0.2']),
% 36.18/36.60 [weight('<53,408,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.409.2.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.409.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_403]).
% 36.18/36.60 cnf('0.410.0.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),not(X2)) = implies(not(X1),not(X2)) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.313.2.0'])).
% 36.18/36.60 cnf('0.410.0.1',plain,
% 36.18/36.60 ( implies(X2,big_hat(X1,X2)) = implies(not(X1),not(X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.410.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.410.0.2',plain,
% 36.18/36.60 ( implies(X2,big_hat(X1,X2)) = implies(X2,X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.410.0.1','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.410.1.0',plain,
% 36.18/36.60 ( implies(X2,big_hat(X1,X2)) = implies(X2,X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.410.0.2']),
% 36.18/36.60 [weight('<53,313,409,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.410.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X1)) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.410.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_404]).
% 36.18/36.60 cnf('0.411.0.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),not(X1)) = implies(not(X2),not(X1)) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.314.2.0'])).
% 36.18/36.60 cnf('0.411.0.1',plain,
% 36.18/36.60 ( implies(X1,big_hat(X1,X2)) = implies(not(X2),not(X1)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.411.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.411.0.2',plain,
% 36.18/36.60 ( implies(X1,big_hat(X1,X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.411.0.1','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.411.1.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X1,X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.411.0.2']),
% 36.18/36.60 [weight('<53,314,409,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.411.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X1,X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.411.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_405]).
% 36.18/36.60 cnf('0.412.0.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,X1)) = implies(implies(X1,X2),big_hat(X2,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.410.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.412.0.1',plain,
% 36.18/36.60 ( X1 = implies(implies(X1,X2),big_hat(X2,X1)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.412.0.0','0.130.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.412.1.0',plain,
% 36.18/36.60 ( X1 = implies(implies(X1,X2),big_hat(X2,X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.412.0.1']),
% 36.18/36.60 [weight('<71,410,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.412.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),big_hat(X2,X1)) = X1 ),
% 36.18/36.60 inference(orient,[status(thm)],['0.412.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_406]).
% 36.18/36.60 cnf('0.413.0.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X1,X2)) = implies(implies(X1,X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.411.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.413.0.1',plain,
% 36.18/36.60 ( X1 = implies(implies(X1,X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.413.0.0','0.127.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.413.1.0',plain,
% 36.18/36.60 ( X1 = implies(implies(X1,X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.413.0.1']),
% 36.18/36.60 [weight('<71,411,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.413.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),big_hat(X1,X2)) = X1 ),
% 36.18/36.60 inference(orient,[status(thm)],['0.413.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_407]).
% 36.18/36.60 cnf('0.415.0.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),implies(implies(X2,big_hat(X2,X1)),X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.108.2.0','0.412.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.415.0.1',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),implies(implies(X2,X1),X1)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.415.0.0','0.411.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2.1','L')]).
% 36.18/36.60 cnf('0.415.0.2',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(X2,X1)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.415.0.1','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.415.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(X2,X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.415.0.2']),
% 36.18/36.60 [weight('<71,412,108,[0,0,0,8]>')]).
% 36.18/36.60 cnf('0.415.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),big_V(X2,X1)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.415.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_409]).
% 36.18/36.60 cnf('0.417.0.0',plain,
% 36.18/36.60 ( truth = implies(not(big_hat(X1,X2)),big_V(not(X2),not(X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.415.2.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.417.0.1',plain,
% 36.18/36.60 ( truth = implies(not(big_hat(X1,X2)),not(big_hat(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.417.0.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.417.0.2',plain,
% 36.18/36.60 ( truth = implies(big_hat(X2,X1),big_hat(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.417.0.1','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.417.1.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(X2,X1),big_hat(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.417.0.2']),
% 36.18/36.60 [weight('<71,415,121,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.417.2.0',plain,
% 36.18/36.60 ( implies(big_hat(X1,X2),big_hat(X2,X1)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.417.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_411]).
% 36.18/36.60 cnf('0.419.0.0',plain,
% 36.18/36.60 ( big_V(not(X1),not(X2)) = implies(implies(X2,X1),not(X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.419.0.1',plain,
% 36.18/36.60 ( not(big_hat(X1,X2)) = implies(implies(X2,X1),not(X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.419.0.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.419.1.0',plain,
% 36.18/36.60 ( not(big_hat(X1,X2)) = implies(implies(X2,X1),not(X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.419.0.1']),
% 36.18/36.60 [weight('<76,409,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.419.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),not(X1)) = not(big_hat(X2,X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.419.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_413]).
% 36.18/36.60 cnf('0.420.0.0',plain,
% 36.18/36.60 ( not(big_hat(X1,not(X2))) = implies(implies(not(X2),X1),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.419.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.420.0.1',plain,
% 36.18/36.60 ( big_V(not(X1),X2) = implies(implies(not(X2),X1),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.420.0.0','0.124.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.420.1.0',plain,
% 36.18/36.60 ( big_V(not(X1),X2) = implies(implies(not(X2),X1),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.420.0.1']),
% 36.18/36.60 [weight('<76,419,114,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.420.2.0',plain,
% 36.18/36.60 ( implies(implies(not(X1),X2),X1) = big_V(not(X2),X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.420.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_414]).
% 36.18/36.60 cnf('0.421.0.0',plain,
% 36.18/36.60 ( not(big_hat(big_hat(X1,X2),implies(X2,X1))) = implies(X2,not(implies(X2,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.419.2.0','0.412.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.421.0.1',plain,
% 36.18/36.60 ( not(big_hat(X1,X2)) = implies(X2,not(implies(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.421.0.0','0.201.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.421.1.0',plain,
% 36.18/36.60 ( not(big_hat(X1,X2)) = implies(X2,not(implies(X2,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.421.0.1']),
% 36.18/36.60 [weight('<76,419,412,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.421.2.0',plain,
% 36.18/36.60 ( implies(X1,not(implies(X1,X2))) = not(big_hat(X2,X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.421.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_415]).
% 36.18/36.60 cnf('0.422.0.0',plain,
% 36.18/36.60 ( big_V(implies(not(X1),X2),X1) = implies(big_V(not(X2),X1),X1) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.420.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.422.0.1',plain,
% 36.18/36.60 ( big_V(implies(not(X1),X2),X1) = implies(not(X2),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.422.0.0','0.32.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.422.1.0',plain,
% 36.18/36.60 ( big_V(implies(not(X1),X2),X1) = implies(not(X2),X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.422.0.1']),
% 36.18/36.60 [weight('<76,420,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.422.1.1',plain,
% 36.18/36.60 ( big_V(X1,implies(not(X1),X2)) = implies(not(X2),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.422.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.422.1.2',plain,
% 36.18/36.60 ( implies(not(X1),X2) = implies(not(X2),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.422.1.1','0.189.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.422.2.0',plain,
% 36.18/36.60 ( implies(not(X1),X2) = implies(not(X2),X1) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.422.1.2']),
% 36.18/36.60 [equation_7]).
% 36.18/36.60 cnf('0.423.0.0',plain,
% 36.18/36.60 ( implies(X1,not(X2)) = implies(X2,not(X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.409.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.423.1.0',plain,
% 36.18/36.60 ( implies(X1,not(X2)) = implies(X2,not(X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.423.0.0']),
% 36.18/36.60 [weight('<80,409,114,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.423.2.0',plain,
% 36.18/36.60 ( implies(X1,not(X2)) = implies(X2,not(X1)) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.423.1.0']),
% 36.18/36.60 [equation_8]).
% 36.18/36.60 cnf('0.424.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X2,X1)) = implies(truth,big_V(X2,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.415.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.424.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X2,X1)) = big_V(X2,X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.424.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.424.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X2,X1)) = big_V(X2,X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.424.0.1']),
% 36.18/36.60 [weight('<87,415,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.424.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X2,X1)) = big_V(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.424.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_416]).
% 36.18/36.60 cnf('0.426.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,X1)) = implies(truth,big_hat(X2,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.417.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.426.0.1',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,X1)) = big_hat(X2,X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.426.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.426.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,X1)) = big_hat(X2,X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.426.0.1']),
% 36.18/36.60 [weight('<87,417,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.426.2.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,X1)) = big_hat(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.426.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_418]).
% 36.18/36.60 cnf('0.429.0.0',plain,
% 36.18/36.60 ( not(X1) = implies(implies(not(X1),not(X2)),not(big_V(X2,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.412.2.0','0.123.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.429.0.1',plain,
% 36.18/36.60 ( not(X1) = implies(implies(X2,X1),not(big_V(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.429.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1','L')]).
% 36.18/36.60 cnf('0.429.1.0',plain,
% 36.18/36.60 ( not(X1) = implies(implies(X2,X1),not(big_V(X2,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.429.0.1']),
% 36.18/36.60 [weight('<98,412,123,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.429.1.1',plain,
% 36.18/36.60 ( not(X1) = implies(big_V(X2,X1),not(implies(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.429.1.0','0.423.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.429.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),not(implies(X1,X2))) = not(X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.429.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_421]).
% 36.18/36.60 cnf('0.430.0.0',plain,
% 36.18/36.60 ( not(X1) = implies(implies(not(X1),not(X2)),not(big_V(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.413.2.0','0.123.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.430.0.1',plain,
% 36.18/36.60 ( not(X1) = implies(implies(X2,X1),not(big_V(X1,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.430.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1','L')]).
% 36.18/36.60 cnf('0.430.1.0',plain,
% 36.18/36.60 ( not(X1) = implies(implies(X2,X1),not(big_V(X1,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.430.0.1']),
% 36.18/36.60 [weight('<98,413,123,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.430.1.1',plain,
% 36.18/36.60 ( not(X1) = implies(big_V(X1,X2),not(implies(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.430.1.0','0.423.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.430.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),not(implies(X2,X1))) = not(X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.430.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_422]).
% 36.18/36.60 cnf('0.447.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(implies(X1,X2),implies(big_hat(X1,X3),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.6.2.0','0.126.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.447.0.1',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(big_hat(X1,X3),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.447.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.447.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(big_hat(X1,X3),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.447.0.1']),
% 36.18/36.60 [weight('<109,126,6,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.447.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(big_hat(X1,X3),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.447.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_439]).
% 36.18/36.60 cnf('0.448.0.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,big_hat(X2,X3)),implies(truth,implies(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.6.2.0','0.126.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.448.0.1',plain,
% 36.18/36.60 ( truth = implies(implies(X1,big_hat(X2,X3)),implies(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.448.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.448.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,big_hat(X2,X3)),implies(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.448.0.1']),
% 36.18/36.60 [weight('<109,126,6,[0,0,0,5]>')]).
% 36.18/36.60 cnf('0.448.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,big_hat(X2,X3)),implies(X1,X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.448.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_440]).
% 36.18/36.60 cnf('0.449.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(implies(X1,X2),implies(big_hat(X3,X1),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.6.2.0','0.129.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.449.0.1',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(big_hat(X3,X1),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.449.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.449.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(big_hat(X3,X1),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.449.0.1']),
% 36.18/36.60 [weight('<109,129,6,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.449.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(big_hat(X3,X1),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.449.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_441]).
% 36.18/36.60 cnf('0.503.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(big_V(X1,X2),implies(implies(big_V(X1,X3),X2),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.159.2.0','0.46.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.503.0.1',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),implies(implies(big_V(X1,X3),X2),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.503.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.503.0.2',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(big_V(X1,X3),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.503.0.1','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.503.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(big_V(X1,X3),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.503.0.2']),
% 36.18/36.60 [weight('<109,159,46,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.503.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.503.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_495]).
% 36.18/36.60 cnf('0.505.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(big_V(X1,X2),implies(implies(big_V(X3,X1),X2),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.159.2.0','0.100.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.505.0.1',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),implies(implies(big_V(X3,X1),X2),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.505.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.505.0.2',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.505.0.1','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.505.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.505.0.2']),
% 36.18/36.60 [weight('<109,159,100,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.505.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),big_V(big_V(X3,X1),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.505.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_497]).
% 36.18/36.60 cnf('0.669.0.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.6.2.0','0.32.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.669.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.669.0.0']),
% 36.18/36.60 [weight('<?,32,6,[0,0,0,5]>')]).
% 36.18/36.60 cnf('0.669.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3))) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.669.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_661]).
% 36.18/36.60 cnf('0.723.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(big_V(big_hat(X1,X2),X3),implies(implies(X1,X3),X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.159.2.0','0.447.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.723.0.1',plain,
% 36.18/36.60 ( truth = implies(big_V(big_hat(X1,X2),X3),implies(implies(X1,X3),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.723.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.723.0.2',plain,
% 36.18/36.60 ( truth = implies(big_V(big_hat(X1,X2),X3),big_V(X1,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.723.0.1','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.723.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(big_hat(X1,X2),X3),big_V(X1,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.723.0.2']),
% 36.18/36.60 [weight('<109,447,159,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.723.2.0',plain,
% 36.18/36.60 ( implies(big_V(big_hat(X1,X2),X3),big_V(X1,X3)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.723.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_715]).
% 36.18/36.60 cnf('0.731.0.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,big_hat(X2,X3)),big_V(X1,X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.503.2.0','0.204.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.731.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,big_hat(X2,X3)),big_V(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.731.0.0']),
% 36.18/36.60 [weight('<109,503,204,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.731.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,big_hat(X2,X3)),big_V(X1,X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.731.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_723]).
% 36.18/36.60 cnf('0.735.0.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(big_V(X3,X2),X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.505.2.0','0.19.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.735.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),big_V(big_V(X3,X2),X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.735.0.0']),
% 36.18/36.60 [weight('<109,505,19,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.735.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),big_V(big_V(X3,X2),X1)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.735.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_727]).
% 36.18/36.60 cnf('0.798.0.0',plain,
% 36.18/36.60 ( implies(big_V(X1,not(X2)),X3) = implies(not(X3),big_hat(not(X1),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.409.2.0','0.119.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.798.1.0',plain,
% 36.18/36.60 ( implies(big_V(X1,not(X2)),X3) = implies(not(X3),big_hat(not(X1),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.798.0.0']),
% 36.18/36.60 [weight('<111,409,119,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.798.2.0',plain,
% 36.18/36.60 ( implies(not(X1),big_hat(not(X2),X3)) = implies(big_V(X2,not(X3)),X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.798.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_790]).
% 36.18/36.60 cnf('0.802.0.0',plain,
% 36.18/36.60 ( implies(big_hat(not(X1),X2),X3) = implies(not(X3),big_V(X1,not(X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.409.2.0','0.122.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.802.1.0',plain,
% 36.18/36.60 ( implies(big_hat(not(X1),X2),X3) = implies(not(X3),big_V(X1,not(X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.802.0.0']),
% 36.18/36.60 [weight('<111,409,122,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.802.2.0',plain,
% 36.18/36.60 ( implies(not(X1),big_V(X2,not(X3))) = implies(big_hat(not(X2),X3),X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.802.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_794]).
% 36.18/36.60 cnf('0.803.0.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,not(X3))) = implies(big_V(not(X2),X3),not(X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.409.2.0','0.124.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.803.1.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,not(X3))) = implies(big_V(not(X2),X3),not(X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.803.0.0']),
% 36.18/36.60 [weight('<111,409,124,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.803.2.0',plain,
% 36.18/36.60 ( implies(big_V(not(X1),X2),not(X3)) = implies(X3,big_hat(X1,not(X2))) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.803.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_795]).
% 36.18/36.60 cnf('0.804.0.0',plain,
% 36.18/36.60 ( implies(big_hat(X1,not(X2)),X3) = implies(not(X3),big_V(not(X1),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.409.2.0','0.124.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.804.1.0',plain,
% 36.18/36.60 ( implies(big_hat(X1,not(X2)),X3) = implies(not(X3),big_V(not(X1),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.804.0.0']),
% 36.18/36.60 [weight('<111,409,124,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.804.2.0',plain,
% 36.18/36.60 ( implies(not(X1),big_V(not(X2),X3)) = implies(big_hat(X2,not(X3)),X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.804.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_796]).
% 36.18/36.60 cnf('0.843.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,not(X2)),not(X3)) = not(big_hat(big_hat(not(X1),X2),X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.122.2.0','0.119.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.1','L')]).
% 36.18/36.60 cnf('0.843.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,not(X2)),not(X3)) = not(big_hat(big_hat(not(X1),X2),X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.843.0.0']),
% 36.18/36.60 [weight('<119,122,119,[1,0,0,2]>')]).
% 36.18/36.60 cnf('0.843.2.0',plain,
% 36.18/36.60 ( not(big_hat(big_hat(not(X1),X2),X3)) = big_V(big_V(X1,not(X2)),not(X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.843.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_835]).
% 36.18/36.60 cnf('0.870.0.0',plain,
% 36.18/36.60 ( big_V(implies(big_V(X1,X2),X3),implies(X1,X3)) = implies(truth,implies(X1,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.46.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.870.0.1',plain,
% 36.18/36.60 ( big_V(implies(big_V(X1,X2),X3),implies(X1,X3)) = implies(X1,X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.870.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.870.1.0',plain,
% 36.18/36.60 ( big_V(implies(big_V(X1,X2),X3),implies(X1,X3)) = implies(X1,X3) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.870.0.1']),
% 36.18/36.60 [weight('<129,46,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.870.1.1',plain,
% 36.18/36.60 ( big_V(implies(X1,X3),implies(big_V(X1,X2),X3)) = implies(X1,X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.870.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.870.2.0',plain,
% 36.18/36.60 ( big_V(implies(X1,X2),implies(big_V(X1,X3),X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.870.1.1',theory(equality)]),
% 36.18/36.60 [u,rule_862]).
% 36.18/36.60 cnf('0.959.0.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(truth,big_hat(implies(big_hat(X3,X1),X2),implies(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.412.2.0','0.449.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.959.0.1',plain,
% 36.18/36.60 ( implies(X1,X2) = big_hat(implies(big_hat(X3,X1),X2),implies(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.959.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.959.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = big_hat(implies(big_hat(X3,X1),X2),implies(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.959.0.1']),
% 36.18/36.60 [weight('<129,449,412,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.959.1.1',plain,
% 36.18/36.60 ( implies(X1,X2) = big_hat(implies(X1,X2),implies(big_hat(X3,X1),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.959.1.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.959.2.0',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(big_hat(X3,X1),X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.959.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_951]).
% 36.18/36.60 cnf('0.1556.0.0',plain,
% 36.18/36.60 ( truth = implies(big_V(not(X1),X2),big_V(implies(X1,X3),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.503.2.0','0.105.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.1556.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(not(X1),X2),big_V(implies(X1,X3),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.1556.0.0']),
% 36.18/36.60 [weight('<131,503,105,[1,0,0,5]>')]).
% 36.18/36.60 cnf('0.1556.2.0',plain,
% 36.18/36.60 ( implies(big_V(not(X1),X2),big_V(implies(X1,X3),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.1556.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_1548]).
% 36.18/36.60 cnf('0.1746.0.0',plain,
% 36.18/36.60 ( truth = implies(not(big_hat(X1,X2)),big_V(implies(X1,X3),not(X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.1556.2.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.1746.0.1',plain,
% 36.18/36.60 ( truth = implies(big_hat(not(implies(X1,X3)),X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.1746.0.0','0.802.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.1746.1.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(not(implies(X1,X3)),X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.1746.0.1']),
% 36.18/36.60 [weight('<131,1556,121,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.1746.2.0',plain,
% 36.18/36.60 ( implies(big_hat(not(implies(X1,X2)),X3),big_hat(X1,X3)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.1746.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_1738]).
% 36.18/36.60 cnf('0.1747.0.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(not(not(big_hat(X1,X2))),X3),big_hat(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.1746.2.0','0.421.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.1.1','L')]).
% 36.18/36.60 cnf('0.1747.0.1',plain,
% 36.18/36.60 ( truth = implies(big_hat(big_hat(X1,X2),X3),big_hat(X2,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.1747.0.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1.1','L')]).
% 36.18/36.60 cnf('0.1747.1.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(big_hat(X1,X2),X3),big_hat(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.1747.0.1']),
% 36.18/36.60 [weight('<109,1746,421,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.1747.2.0',plain,
% 36.18/36.60 ( implies(big_hat(big_hat(X1,X2),X3),big_hat(X2,X3)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.1747.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_1739]).
% 36.18/36.60 cnf('0.1748.0.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(not(not(X1)),X2),big_hat(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.1746.2.0','0.429.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.1.1','L')]).
% 36.18/36.60 cnf('0.1748.0.1',plain,
% 36.18/36.60 ( truth = implies(big_hat(X1,X2),big_hat(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.1748.0.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1.1','L')]).
% 36.18/36.60 cnf('0.1748.1.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(X1,X2),big_hat(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.1748.0.1']),
% 36.18/36.60 [weight('<109,1746,429,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.1748.2.0',plain,
% 36.18/36.60 ( implies(big_hat(X1,X2),big_hat(big_V(X3,X1),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.1748.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_1740]).
% 36.18/36.60 cnf('0.1756.0.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.1747.2.0','0.199.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.1756.1.0',plain,
% 36.18/36.60 ( truth = implies(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.1756.0.0']),
% 36.18/36.60 [weight('<109,1747,199,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.1756.2.0',plain,
% 36.18/36.60 ( implies(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.1756.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_1748]).
% 36.18/36.60 cnf('0.1816.0.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = implies(truth,big_hat(big_hat(big_V(X3,X1),X2),big_hat(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.412.2.0','0.1748.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.1816.0.1',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(big_V(X3,X1),X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.1816.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.1816.1.0',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(big_V(X3,X1),X2),big_hat(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.1816.0.1']),
% 36.18/36.60 [weight('<129,1748,412,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.1816.1.1',plain,
% 36.18/36.60 ( big_hat(X1,X2) = big_hat(big_hat(X1,X2),big_hat(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.1816.1.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.1816.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),big_hat(big_V(X3,X1),X2)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.1816.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_1808]).
% 36.18/36.60 cnf('0.2206.0.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),X3) = big_hat(big_hat(big_V(X1,X2),X3),big_V(X2,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.197.2.0','0.424.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.2206.1.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),X3) = big_hat(big_hat(big_V(X1,X2),X3),big_V(X2,X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2206.0.0']),
% 36.18/36.60 [weight('<149,424,197,[0,0,0,4]>')]).
% 36.18/36.60 cnf('0.2206.1.1',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),X3) = big_hat(big_V(X2,X1),big_hat(big_V(X1,X2),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2206.1.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2206.2.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),big_hat(big_V(X2,X1),X3)) = big_hat(big_V(X2,X1),X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2206.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_2198]).
% 36.18/36.60 cnf('0.2207.0.0',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,X3)) = big_hat(big_hat(X1,big_V(X2,X3)),big_V(X3,X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.198.2.0','0.424.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.2207.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,X3)) = big_hat(big_hat(X1,big_V(X2,X3)),big_V(X3,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2207.0.0']),
% 36.18/36.60 [weight('<149,424,198,[0,0,0,4]>')]).
% 36.18/36.60 cnf('0.2207.1.1',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,X3)) = big_hat(big_V(X3,X2),big_hat(X1,big_V(X2,X3))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2207.1.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2207.2.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),big_hat(X3,big_V(X2,X1))) = big_hat(X3,big_V(X2,X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2207.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_2199]).
% 36.18/36.60 cnf('0.2208.0.0',plain,
% 36.18/36.60 ( big_V(big_V(big_hat(X1,X2),big_hat(X2,X1)),X3) = big_V(big_hat(X1,X2),big_V(big_hat(X2,X1),X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.88.2.0','0.426.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.2208.0.1',plain,
% 36.18/36.60 ( big_V(big_hat(X2,X1),X3) = big_V(big_hat(X1,X2),big_V(big_hat(X2,X1),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2208.0.0','0.426.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2208.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(X2,X1),X3) = big_V(big_hat(X1,X2),big_V(big_hat(X2,X1),X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2208.0.1']),
% 36.18/36.60 [weight('<149,426,88,[0,0,0,3]>')]).
% 36.18/36.60 cnf('0.2208.2.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_V(big_hat(X2,X1),X3)) = big_V(big_hat(X2,X1),X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2208.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2200]).
% 36.18/36.60 cnf('0.2209.0.0',plain,
% 36.18/36.60 ( big_V(X1,big_V(big_hat(X2,X3),big_hat(X3,X2))) = big_V(big_hat(X2,X3),big_V(X1,big_hat(X3,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.89.2.0','0.426.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.2209.0.1',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X3,X2)) = big_V(big_hat(X2,X3),big_V(X1,big_hat(X3,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2209.0.0','0.426.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.2209.1.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X3,X2)) = big_V(big_hat(X2,X3),big_V(X1,big_hat(X3,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2209.0.1']),
% 36.18/36.60 [weight('<149,426,89,[0,0,0,4]>')]).
% 36.18/36.60 cnf('0.2209.2.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_V(X3,big_hat(X2,X1))) = big_V(X3,big_hat(X2,X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2209.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2201]).
% 36.18/36.60 cnf('0.2214.0.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = implies(truth,big_hat(implies(X1,X2),implies(X1,big_hat(X2,X3)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.412.2.0','0.448.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2214.0.1',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = big_hat(implies(X1,X2),implies(X1,big_hat(X2,X3))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2214.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2214.1.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = big_hat(implies(X1,X2),implies(X1,big_hat(X2,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2214.0.1']),
% 36.18/36.60 [weight('<149,448,412,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2214.2.0',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(X1,big_hat(X2,X3))) = implies(X1,big_hat(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2214.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2206]).
% 36.18/36.60 cnf('0.2217.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = implies(truth,big_V(big_V(X1,X3),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.503.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2217.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2217.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2217.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2217.0.1']),
% 36.18/36.60 [weight('<149,503,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2217.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2217.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_2209]).
% 36.18/36.60 cnf('0.2218.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X1),X2)) = implies(truth,big_V(big_V(X3,X1),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.505.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2218.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X1),X2)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2218.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2218.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X1),X2)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2218.0.1']),
% 36.18/36.60 [weight('<149,505,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2218.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X1),X2)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2218.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_2210]).
% 36.18/36.60 cnf('0.2223.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),X3) = implies(truth,big_hat(big_V(X1,X3),big_V(big_hat(X1,X2),X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.412.2.0','0.723.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2223.0.1',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),X3) = big_hat(big_V(X1,X3),big_V(big_hat(X1,X2),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2223.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2223.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),X3) = big_hat(big_V(X1,X3),big_V(big_hat(X1,X2),X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2223.0.1']),
% 36.18/36.60 [weight('<149,723,412,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2223.2.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),big_V(big_hat(X1,X3),X2)) = big_V(big_hat(X1,X3),X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2223.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2215]).
% 36.18/36.60 cnf('0.2229.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X2),X1)) = implies(truth,big_V(big_V(X3,X2),X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.735.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2229.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X2),X1)) = big_V(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2229.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2229.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X2),X1)) = big_V(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2229.0.1']),
% 36.18/36.60 [weight('<149,735,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2229.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X2),X1)) = big_V(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2229.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_2221]).
% 36.18/36.60 cnf('0.2249.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) = implies(truth,big_hat(X2,big_V(X3,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.1756.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2249.0.1',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) = big_hat(X2,big_V(X3,X1)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2249.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2249.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) = big_hat(X2,big_V(X3,X1)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2249.0.1']),
% 36.18/36.60 [weight('<149,1756,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2249.2.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X2,big_V(X3,X1))) = big_hat(X2,big_V(X3,X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2249.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_2241]).
% 36.18/36.60 cnf('0.2352.0.0',plain,
% 36.18/36.60 ( implies(implies(big_V(X1,X2),X2),implies(X3,X2)) = big_V(implies(X3,big_V(X1,X2)),implies(implies(X1,X2),implies(X3,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.57.2.0','0.32.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.2352.0.1',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(X3,X2)) = big_V(implies(X3,big_V(X1,X2)),implies(implies(X1,X2),implies(X3,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2352.0.0','0.32.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2352.1.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(X3,X2)) = big_V(implies(X3,big_V(X1,X2)),implies(implies(X1,X2),implies(X3,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2352.0.1']),
% 36.18/36.60 [weight('<?,57,32,[1,0,0,5]>')]).
% 36.18/36.60 cnf('0.2352.2.0',plain,
% 36.18/36.60 ( big_V(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3))) = implies(implies(X2,X3),implies(X1,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2352.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2344]).
% 36.18/36.60 cnf('0.2521.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(big_V(X1,X2),implies(big_hat(implies(X1,X2),X3),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.159.2.0','0.126.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2521.0.1',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),implies(big_hat(implies(X1,X2),X3),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2521.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2521.1.0',plain,
% 36.18/36.60 ( truth = implies(big_V(X1,X2),implies(big_hat(implies(X1,X2),X3),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2521.0.1']),
% 36.18/36.60 [weight('<155,159,126,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.2521.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),implies(big_hat(implies(X1,X2),X3),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2521.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2513]).
% 36.18/36.60 cnf('0.2522.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(X1,implies(big_hat(implies(X1,X2),X3),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.46.2.0','0.2521.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2522.0.1',plain,
% 36.18/36.60 ( truth = implies(X1,implies(big_hat(implies(X1,X2),X3),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2522.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2522.1.0',plain,
% 36.18/36.60 ( truth = implies(X1,implies(big_hat(implies(X1,X2),X3),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2522.0.1']),
% 36.18/36.60 [weight('<109,2521,46,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2522.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(big_hat(implies(X1,X2),X3),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2522.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2514]).
% 36.18/36.60 cnf('0.2524.0.0',plain,
% 36.18/36.60 ( truth = implies(X1,implies(big_hat(X2,implies(X1,X3)),X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.2522.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.2524.1.0',plain,
% 36.18/36.60 ( truth = implies(X1,implies(big_hat(X2,implies(X1,X3)),X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2524.0.0']),
% 36.18/36.60 [weight('<109,2522,28,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.2524.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(big_hat(X2,implies(X1,X3)),X3)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2524.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_2516]).
% 36.18/36.60 cnf('0.2527.0.0',plain,
% 36.18/36.60 ( X1 = implies(truth,big_hat(implies(big_hat(X2,implies(X1,X3)),X3),X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.412.2.0','0.2524.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.2527.0.1',plain,
% 36.18/36.60 ( X1 = big_hat(implies(big_hat(X2,implies(X1,X3)),X3),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2527.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2527.1.0',plain,
% 36.18/36.60 ( X1 = big_hat(implies(big_hat(X2,implies(X1,X3)),X3),X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.2527.0.1']),
% 36.18/36.60 [weight('<109,2524,412,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.2527.1.1',plain,
% 36.18/36.60 ( X1 = big_hat(X1,implies(big_hat(X2,implies(X1,X3)),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.2527.1.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.2527.2.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(big_hat(X2,implies(X1,X3)),X3)) = X1 ),
% 36.18/36.60 inference(orient,[status(thm)],['0.2527.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_2519]).
% 36.18/36.60 cnf('0.4723.0.0',plain,
% 36.18/36.60 ( truth = implies(truth,implies(implies(X1,X2),implies(big_V(X1,big_hat(X2,X3)),X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.669.2.0','0.731.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4723.0.1',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(big_V(X1,big_hat(X2,X3)),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4723.0.0','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4723.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(X1,X2),implies(big_V(X1,big_hat(X2,X3)),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4723.0.1']),
% 36.18/36.60 [weight('<155,731,669,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.4723.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(big_V(X1,big_hat(X2,X3)),X2)) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4723.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4715]).
% 36.18/36.60 cnf('0.4724.0.0',plain,
% 36.18/36.60 ( big_V(implies(X1,X2),implies(big_V(X1,big_hat(X2,X3)),X2)) = implies(truth,implies(big_V(X1,big_hat(X2,X3)),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.4723.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4724.0.1',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(truth,implies(big_V(X1,big_hat(X2,X3)),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4724.0.0','0.870.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4724.0.2',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(big_V(X1,big_hat(X2,X3)),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4724.0.1','0.1.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4724.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(big_V(X1,big_hat(X2,X3)),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4724.0.2']),
% 36.18/36.60 [weight('<87,4723,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.4724.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,big_hat(X2,X3)),X2) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4724.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4716]).
% 36.18/36.60 cnf('0.4725.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,big_hat(X2,X3)),X2) = implies(implies(X1,X2),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.4724.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4725.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,big_hat(X2,X3)),X2) = big_V(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4725.0.0','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4725.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,big_hat(X2,X3)),X2) = big_V(X1,X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4725.0.1']),
% 36.18/36.60 [weight('<87,4724,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.4725.1.1',plain,
% 36.18/36.60 ( big_V(X2,big_V(X1,big_hat(X2,X3))) = big_V(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4725.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4725.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_V(X2,big_hat(X1,X3))) = big_V(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4725.1.1',theory(equality)]),
% 36.18/36.60 [u,rule_4717]).
% 36.18/36.60 cnf('0.4727.0.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(big_V(X1,big_hat(X3,X2)),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4724.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.2','L')]).
% 36.18/36.60 cnf('0.4727.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(big_V(X1,big_hat(X3,X2)),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4727.0.0']),
% 36.18/36.60 [weight('<87,4724,28,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.4727.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,big_hat(X2,X3)),X3) = implies(X1,X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4727.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4719]).
% 36.18/36.60 cnf('0.4729.0.0',plain,
% 36.18/36.60 ( big_V(X1,X2) = big_V(X2,big_V(X1,big_hat(X3,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4725.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.4729.1.0',plain,
% 36.18/36.60 ( big_V(X1,X2) = big_V(X2,big_V(X1,big_hat(X3,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4729.0.0']),
% 36.18/36.60 [weight('<87,4725,28,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.4729.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_V(X2,big_hat(X3,X1))) = big_V(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4729.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4721]).
% 36.18/36.60 cnf('0.4733.0.0',plain,
% 36.18/36.60 ( implies(X1,big_V(X2,X3)) = implies(big_V(X1,X3),big_V(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4727.2.0','0.135.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.2','L')]).
% 36.18/36.60 cnf('0.4733.1.0',plain,
% 36.18/36.60 ( implies(X1,big_V(X2,X3)) = implies(big_V(X1,X3),big_V(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4733.0.0']),
% 36.18/36.60 [weight('<103,4727,135,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.4733.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),big_V(X3,X2)) = implies(X1,big_V(X3,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4733.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4725]).
% 36.18/36.60 cnf('0.4734.0.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,X3)) = implies(big_V(X1,X3),implies(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4727.2.0','0.136.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.2','L')]).
% 36.18/36.60 cnf('0.4734.1.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,X3)) = implies(big_V(X1,X3),implies(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4734.0.0']),
% 36.18/36.60 [weight('<103,4727,136,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.4734.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),implies(X3,X2)) = implies(X1,implies(X3,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4734.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4726]).
% 36.18/36.60 cnf('0.4735.0.0',plain,
% 36.18/36.60 ( big_V(X1,big_V(X2,X3)) = big_V(big_V(X2,X3),big_V(X1,X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4729.2.0','0.134.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.4735.1.0',plain,
% 36.18/36.60 ( big_V(X1,big_V(X2,X3)) = big_V(big_V(X2,X3),big_V(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4735.0.0']),
% 36.18/36.60 [weight('<103,4729,134,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.4735.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X3,X1)) = big_V(X3,big_V(X1,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4735.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4727]).
% 36.18/36.60 cnf('0.4736.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X2),X1)) = big_V(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.2229.2.0'])).
% 36.18/36.60 cnf('0.4736.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X3,X2),big_V(X1,X2)) = big_V(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4736.0.0','0.4735.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4736.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X3,X2),big_V(X1,X2)) = big_V(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4736.0.1']),
% 36.18/36.60 [weight('<103,2229,4735,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.4736.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X3,X2)) = big_V(big_V(X1,X2),X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4736.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_4728]).
% 36.18/36.60 cnf('0.4737.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X3,X1),X2)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.2218.2.0'])).
% 36.18/36.60 cnf('0.4737.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X3,X1)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4737.0.0','0.4736.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4737.0.2',plain,
% 36.18/36.60 ( big_V(X3,big_V(X1,X2)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4737.0.1','0.4735.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4737.1.0',plain,
% 36.18/36.60 ( big_V(X3,big_V(X1,X2)) = big_V(big_V(X3,X1),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4737.0.2']),
% 36.18/36.60 [weight('<65,2218,4736,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.4737.2.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),X3) = big_V(X1,big_V(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4737.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4729]).
% 36.18/36.60 cnf('0.4738.0.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.2217.2.0'])).
% 36.18/36.60 cnf('0.4738.0.1',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X1,X3)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4738.0.0','0.4736.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4738.1.0',plain,
% 36.18/36.60 ( big_V(big_V(X1,X2),big_V(X1,X3)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4738.0.1']),
% 36.18/36.60 [weight('<103,2217,4736,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.4738.1.1',plain,
% 36.18/36.60 ( big_V(X1,big_V(X2,big_V(X1,X3))) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4738.1.0','0.4737.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4738.1.2',plain,
% 36.18/36.60 ( big_V(X2,big_V(X1,X3)) = big_V(big_V(X1,X3),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4738.1.1','0.89.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4738.1.3',plain,
% 36.18/36.60 ( big_V(X2,big_V(X1,X3)) = big_V(X1,big_V(X3,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4738.1.2','0.4737.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4738.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_V(X2,X3)) = big_V(X2,big_V(X3,X1)) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.4738.1.3']),
% 36.18/36.60 [equation_9]).
% 36.18/36.60 cnf('0.4744.0.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),X3) = implies(big_V(X1,big_V(X2,X3)),X3) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.32.2.0','0.4737.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4744.1.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),X3) = implies(big_V(X1,big_V(X2,X3)),X3) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4744.0.0']),
% 36.18/36.60 [weight('<103,4737,32,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.4744.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,big_V(X2,X3)),X3) = implies(big_V(X1,X2),X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4744.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4733]).
% 36.18/36.60 cnf('0.4750.0.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(X2,big_hat(X1,not(big_hat(not(X2),X3)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4724.2.0','0.803.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4750.0.1',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(X2,big_hat(X1,not(big_hat(not(X2),X3)))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4750.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4750.0.2',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(X2,big_hat(X1,big_V(X2,not(X3)))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4750.0.1','0.122.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2.2','L')]).
% 36.18/36.60 cnf('0.4750.1.0',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(X2,big_hat(X1,big_V(X2,not(X3)))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4750.0.2']),
% 36.18/36.60 [weight('<107,4724,803,[1,0,0,0]>')]).
% 36.18/36.60 cnf('0.4750.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,big_V(X1,not(X3)))) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4750.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4739]).
% 36.18/36.60 cnf('0.4751.0.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(X1,big_hat(X2,big_V(X1,X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4750.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2.2','L')]).
% 36.18/36.60 cnf('0.4751.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(X1,big_hat(X2,big_V(X1,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4751.0.0']),
% 36.18/36.60 [weight('<87,4750,114,[1,0,0,6]>')]).
% 36.18/36.60 cnf('0.4751.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,big_V(X1,X3))) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4751.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4740]).
% 36.18/36.60 cnf('0.4764.0.0',plain,
% 36.18/36.60 ( not(big_hat(big_hat(not(X1),X2),X3)) = big_V(big_V(X1,not(X2)),not(X3)) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.843.2.0'])).
% 36.18/36.60 cnf('0.4764.0.1',plain,
% 36.18/36.60 ( not(big_hat(big_hat(not(X1),X2),X3)) = big_V(X1,big_V(not(X2),not(X3))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4764.0.0','0.4737.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4764.0.2',plain,
% 36.18/36.60 ( not(big_hat(big_hat(not(X1),X2),X3)) = big_V(X1,not(big_hat(X2,X3))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4764.0.1','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.4764.1.0',plain,
% 36.18/36.60 ( not(big_hat(big_hat(not(X1),X2),X3)) = big_V(X1,not(big_hat(X2,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4764.0.2']),
% 36.18/36.60 [weight('<111,843,4737,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.4764.2.0',plain,
% 36.18/36.60 ( not(big_hat(big_hat(not(X1),X2),X3)) = big_V(X1,not(big_hat(X2,X3))) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4764.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_4753]).
% 36.18/36.60 cnf('0.4765.0.0',plain,
% 36.18/36.60 ( big_hat(big_hat(not(X1),X2),X3) = not(big_V(X1,not(big_hat(X2,X3)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.114.2.0','0.4764.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4765.0.1',plain,
% 36.18/36.60 ( big_hat(big_hat(not(X1),X2),X3) = big_hat(not(X1),big_hat(X2,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4765.0.0','0.119.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4765.1.0',plain,
% 36.18/36.60 ( big_hat(big_hat(not(X1),X2),X3) = big_hat(not(X1),big_hat(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4765.0.1']),
% 36.18/36.60 [weight('<90,4764,114,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.4765.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(not(X1),X2),X3) = big_hat(not(X1),big_hat(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4765.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_4754]).
% 36.18/36.60 cnf('0.4766.0.0',plain,
% 36.18/36.60 ( big_hat(not(not(X1)),big_hat(X2,X3)) = big_hat(big_hat(X1,X2),X3) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4765.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.1','L')]).
% 36.18/36.60 cnf('0.4766.0.1',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,X3)) = big_hat(big_hat(X1,X2),X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4766.0.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4766.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,X3)) = big_hat(big_hat(X1,X2),X3) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4766.0.1']),
% 36.18/36.60 [weight('<65,4765,114,[1,0,0,2]>')]).
% 36.18/36.60 cnf('0.4766.2.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),X3) = big_hat(X1,big_hat(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4766.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4755]).
% 36.18/36.60 cnf('0.4769.0.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),implies(X3,X1)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.201.2.0'])).
% 36.18/36.60 cnf('0.4769.0.1',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,implies(X3,X1))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4769.0.0','0.4766.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4769.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,implies(X3,X1))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4769.0.1']),
% 36.18/36.60 [weight('<87,201,4766,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.4769.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,implies(X3,X1))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4769.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_4758]).
% 36.18/36.60 cnf('0.4770.0.0',plain,
% 36.18/36.60 ( big_hat(big_hat(X1,X2),big_hat(big_V(X3,X1),X2)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.1816.2.0'])).
% 36.18/36.60 cnf('0.4770.0.1',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,big_hat(big_V(X3,X1),X2))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4770.0.0','0.4766.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4770.0.2',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(big_V(X3,X1),X2)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4770.0.1','0.138.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.4770.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(big_V(X3,X1),X2)) = big_hat(X1,X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4770.0.2']),
% 36.18/36.60 [weight('<87,1816,4766,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.4770.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(big_V(X2,X1),X3)) = big_hat(X1,X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4770.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_4759]).
% 36.18/36.60 cnf('0.4773.0.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = implies(X1,big_hat(X2,big_hat(X3,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.410.2.0','0.4766.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.4773.1.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = implies(X1,big_hat(X2,big_hat(X3,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4773.0.0']),
% 36.18/36.60 [weight('<103,4766,410,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.4773.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,big_hat(X3,X1))) = implies(X1,big_hat(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4773.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4762]).
% 36.18/36.60 cnf('0.4774.0.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = implies(X1,big_hat(big_hat(X3,X1),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4773.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.4774.0.1',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = implies(X1,big_hat(X3,big_hat(X1,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4774.0.0','0.4766.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.4774.1.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,X3)) = implies(X1,big_hat(X3,big_hat(X1,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4774.0.1']),
% 36.18/36.60 [weight('<103,4773,28,[1,0,0,2]>')]).
% 36.18/36.60 cnf('0.4774.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,big_hat(X1,X3))) = implies(X1,big_hat(X3,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4774.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4763]).
% 36.18/36.60 cnf('0.4793.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_V(X3,big_hat(X2,X1))) = big_V(big_hat(X1,X2),X3) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4738.2.0','0.2208.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4793.0.1',plain,
% 36.18/36.60 ( big_V(X3,big_hat(X2,X1)) = big_V(big_hat(X1,X2),X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4793.0.0','0.2209.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4793.1.0',plain,
% 36.18/36.60 ( big_V(X3,big_hat(X2,X1)) = big_V(big_hat(X1,X2),X3) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4793.0.1']),
% 36.18/36.60 [weight('<120,4738,2208,[1,0,0,0]>')]).
% 36.18/36.60 cnf('0.4793.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,X3)) = big_V(big_hat(X3,X2),X1) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.4793.1.0']),
% 36.18/36.60 [equation_14]).
% 36.18/36.60 cnf('0.4794.0.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,X3)) = big_hat(X3,big_hat(X1,X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4766.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4794.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,X3)) = big_hat(X3,big_hat(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4794.0.0']),
% 36.18/36.60 [weight('<120,4766,28,[1,0,0,0]>')]).
% 36.18/36.60 cnf('0.4794.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,X3)) = big_hat(X3,big_hat(X1,X2)) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.4794.1.0']),
% 36.18/36.60 [equation_15]).
% 36.18/36.60 cnf('0.4797.0.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,X2),big_hat(X3,big_V(X2,X1))) = big_hat(big_V(X1,X2),X3) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4794.2.0','0.2206.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4797.0.1',plain,
% 36.18/36.60 ( big_hat(X3,big_V(X2,X1)) = big_hat(big_V(X1,X2),X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4797.0.0','0.2207.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4797.1.0',plain,
% 36.18/36.60 ( big_hat(X3,big_V(X2,X1)) = big_hat(big_V(X1,X2),X3) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4797.0.1']),
% 36.18/36.60 [weight('<120,4794,2206,[1,1,0,0]>')]).
% 36.18/36.60 cnf('0.4797.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,X3)) = big_hat(big_V(X3,X2),X1) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.4797.1.0']),
% 36.18/36.60 [equation_18]).
% 36.18/36.60 cnf('0.4798.0.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,X3)) = implies(big_V(X1,not(X2)),implies(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4727.2.0','0.142.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.2','L')]).
% 36.18/36.60 cnf('0.4798.1.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,X3)) = implies(big_V(X1,not(X2)),implies(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4798.0.0']),
% 36.18/36.60 [weight('<125,4727,142,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.4798.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,not(X2)),implies(X2,X3)) = implies(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4798.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4780]).
% 36.18/36.60 cnf('0.4848.0.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,big_V(big_hat(X1,X2),X3))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4766.2.0','0.134.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.4848.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,big_V(big_hat(X1,X2),X3))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4848.0.0']),
% 36.18/36.60 [weight('<129,4766,134,[1,0,0,0]>')]).
% 36.18/36.60 cnf('0.4848.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_hat(X2,big_V(big_hat(X1,X2),X3))) = big_hat(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4848.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_4830]).
% 36.18/36.60 cnf('0.4855.0.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(big_V(big_hat(X2,X1),X3),X2)) = implies(X1,big_hat(X2,X1)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4774.2.0','0.4848.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.4855.0.1',plain,
% 36.18/36.60 ( implies(X1,big_hat(big_V(big_hat(X2,X1),X3),X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4855.0.0','0.410.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.4855.1.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(big_V(big_hat(X2,X1),X3),X2)) = implies(X1,X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4855.0.1']),
% 36.18/36.60 [weight('<129,4848,4774,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.4855.1.1',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,big_V(X3,big_hat(X2,X1)))) = implies(X1,X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.4855.1.0','0.4797.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','R')]).
% 36.18/36.60 cnf('0.4855.2.0',plain,
% 36.18/36.60 ( implies(X1,big_hat(X2,big_V(X3,big_hat(X2,X1)))) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4855.1.1',theory(equality)]),
% 36.18/36.60 [u,rule_4837]).
% 36.18/36.60 cnf('0.4870.0.0',plain,
% 36.18/36.60 ( implies(not(X1),implies(X2,X3)) = implies(not(big_hat(X1,X2)),implies(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4798.2.0','0.121.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.4870.1.0',plain,
% 36.18/36.60 ( implies(not(X1),implies(X2,X3)) = implies(not(big_hat(X1,X2)),implies(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.4870.0.0']),
% 36.18/36.60 [weight('<134,4798,121,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.4870.2.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),implies(X2,X3)) = implies(not(X1),implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.4870.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_4852]).
% 36.18/36.60 cnf('0.5246.0.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),big_hat(X2,X1)) = big_hat(X1,implies(big_hat(X3,implies(X1,X2)),big_hat(X2,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.959.2.0','0.412.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.5246.0.1',plain,
% 36.18/36.60 ( X1 = big_hat(X1,implies(big_hat(X3,implies(X1,X2)),big_hat(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5246.0.0','0.412.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.5246.1.0',plain,
% 36.18/36.60 ( X1 = big_hat(X1,implies(big_hat(X3,implies(X1,X2)),big_hat(X2,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5246.0.1']),
% 36.18/36.60 [weight('<155,959,412,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.5246.2.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(big_hat(X2,implies(X1,X3)),big_hat(X3,X1))) = X1 ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5246.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_5228]).
% 36.18/36.60 cnf('0.5247.0.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,X3)) = big_hat(big_hat(X1,implies(X2,X3)),implies(X2,big_hat(X3,big_hat(X1,implies(X2,X3))))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5246.2.0','0.2527.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.5247.0.1',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,X3)) = big_hat(X1,big_hat(implies(X2,X3),implies(X2,big_hat(X3,big_hat(X1,implies(X2,X3)))))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5247.0.0','0.4766.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.5247.0.2',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,X3)) = big_hat(X1,implies(X2,big_hat(X3,big_hat(X1,implies(X2,X3))))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5247.0.1','0.2214.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.5247.0.3',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,X3)) = big_hat(X1,implies(X2,big_hat(X3,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5247.0.2','0.4769.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2.2','L')]).
% 36.18/36.60 cnf('0.5247.1.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,X3)) = big_hat(X1,implies(X2,big_hat(X3,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5247.0.3']),
% 36.18/36.60 [weight('<103,5246,2527,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.5247.2.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,big_hat(X3,X1))) = big_hat(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5247.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_5229]).
% 36.18/36.60 cnf('0.5253.0.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,big_hat(X3,X1))) = implies(X1,big_hat(X1,implies(X2,X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.411.2.0','0.5247.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.5253.0.1',plain,
% 36.18/36.60 ( implies(X1,implies(X2,big_hat(X3,X1))) = implies(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5253.0.0','0.411.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.5253.1.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,big_hat(X3,X1))) = implies(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5253.0.1']),
% 36.18/36.60 [weight('<103,5247,411,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.5253.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,big_hat(X3,X1))) = implies(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5253.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_5235]).
% 36.18/36.60 cnf('0.5267.0.0',plain,
% 36.18/36.60 ( implies(X1,implies(not(X2),not(X3))) = implies(X1,implies(big_V(X3,not(X1)),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5253.2.0','0.798.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.5267.0.1',plain,
% 36.18/36.60 ( implies(X1,implies(X3,X2)) = implies(X1,implies(big_V(X3,not(X1)),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5267.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.5267.1.0',plain,
% 36.18/36.60 ( implies(X1,implies(X3,X2)) = implies(X1,implies(big_V(X3,not(X1)),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5267.0.1']),
% 36.18/36.60 [weight('<125,5253,798,[1,0,0,2]>')]).
% 36.18/36.60 cnf('0.5267.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(big_V(X2,not(X1)),X3)) = implies(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5267.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_5249]).
% 36.18/36.60 cnf('0.5298.0.0',plain,
% 36.18/36.60 ( implies(X1,implies(not(X2),X3)) = implies(X1,implies(not(big_hat(X3,X1)),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5253.2.0','0.422.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.5298.1.0',plain,
% 36.18/36.60 ( implies(X1,implies(not(X2),X3)) = implies(X1,implies(not(big_hat(X3,X1)),X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5298.0.0']),
% 36.18/36.60 [weight('<134,5253,422,[1,0,0,2]>')]).
% 36.18/36.60 cnf('0.5298.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(not(big_hat(X2,X1)),X3)) = implies(X1,implies(not(X3),X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5298.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_5280]).
% 36.18/36.60 cnf('0.5304.0.0',plain,
% 36.18/36.60 ( implies(not(X1),implies(X2,X3)) = implies(not(X1),implies(big_V(X2,X1),X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5267.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1.2','L')]).
% 36.18/36.60 cnf('0.5304.1.0',plain,
% 36.18/36.60 ( implies(not(X1),implies(X2,X3)) = implies(not(X1),implies(big_V(X2,X1),X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5304.0.0']),
% 36.18/36.60 [weight('<134,5267,114,[1,0,0,5]>')]).
% 36.18/36.60 cnf('0.5304.2.0',plain,
% 36.18/36.60 ( implies(not(X1),implies(big_V(X2,X1),X3)) = implies(not(X1),implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5304.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_5286]).
% 36.18/36.60 cnf('0.5321.0.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,big_hat(X3,big_V(X4,X1)))) = big_hat(X1,big_hat(big_V(X4,X1),implies(X2,X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4770.2.0','0.5247.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.5321.0.1',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,big_hat(X3,big_V(X4,X1)))) = big_hat(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.5321.0.0','0.4770.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.5321.1.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,big_hat(X3,big_V(X4,X1)))) = big_hat(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.5321.0.1']),
% 36.18/36.60 [weight('<149,5247,4770,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.5321.2.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(X2,big_hat(X3,big_V(X4,X1)))) = big_hat(X1,implies(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.5321.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_5303]).
% 36.18/36.60 cnf('0.7339.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X1,X3)) = big_hat(X1,big_V(big_hat(X1,X2),big_hat(X1,X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.2223.2.0','0.127.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.7339.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(X1,X2),big_hat(X1,X3)) = big_hat(X1,big_V(big_hat(X1,X2),big_hat(X1,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7339.0.0']),
% 36.18/36.60 [weight('<169,2223,127,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.7339.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_V(big_hat(X1,X2),big_hat(X1,X3))) = big_V(big_hat(X1,X2),big_hat(X1,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7339.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7317]).
% 36.18/36.60 cnf('0.7340.0.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(X1,big_V(big_hat(X2,X3),big_hat(X2,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.4855.2.0','0.7339.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.7340.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(X1,big_V(big_hat(X2,X3),big_hat(X2,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7340.0.0']),
% 36.18/36.60 [weight('<129,7339,4855,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.7340.2.0',plain,
% 36.18/36.60 ( implies(X1,big_V(big_hat(X2,X3),big_hat(X2,X1))) = implies(X1,X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7340.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7318]).
% 36.18/36.60 cnf('0.7359.0.0',plain,
% 36.18/36.60 ( implies(not(X1),not(X2)) = implies(not(X1),big_V(big_hat(not(X2),X3),not(big_V(X2,X1)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.7340.2.0','0.123.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.7359.0.1',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(not(X1),big_V(big_hat(not(X2),X3),not(big_V(X2,X1)))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7359.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.7359.0.2',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(big_hat(not(big_hat(not(X2),X3)),big_V(X2,X1)),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7359.0.1','0.802.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.7359.0.3',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(big_hat(big_V(X2,not(X3)),big_V(X2,X1)),X1) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7359.0.2','0.122.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1.1','L')]).
% 36.18/36.60 cnf('0.7359.1.0',plain,
% 36.18/36.60 ( implies(X2,X1) = implies(big_hat(big_V(X2,not(X3)),big_V(X2,X1)),X1) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7359.0.3']),
% 36.18/36.60 [weight('<153,7340,123,[1,0,0,6]>')]).
% 36.18/36.60 cnf('0.7359.2.0',plain,
% 36.18/36.60 ( implies(big_hat(big_V(X1,not(X2)),big_V(X1,X3)),X3) = implies(X1,X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7359.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7337]).
% 36.18/36.60 cnf('0.7360.0.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(big_hat(big_V(X1,X3),big_V(X1,X2)),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.7359.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.1.2','L')]).
% 36.18/36.60 cnf('0.7360.1.0',plain,
% 36.18/36.60 ( implies(X1,X2) = implies(big_hat(big_V(X1,X3),big_V(X1,X2)),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7360.0.0']),
% 36.18/36.60 [weight('<129,7359,114,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.7360.2.0',plain,
% 36.18/36.60 ( implies(big_hat(big_V(X1,X2),big_V(X1,X3)),X3) = implies(X1,X3) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7360.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7338]).
% 36.18/36.60 cnf('0.7361.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(big_V(X1,X2),big_V(X1,X3)),X3) = implies(implies(X1,X3),X3) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.7360.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.7361.0.1',plain,
% 36.18/36.60 ( big_V(big_hat(big_V(X1,X2),big_V(X1,X3)),X3) = big_V(X1,X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7361.0.0','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.7361.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(big_V(X1,X2),big_V(X1,X3)),X3) = big_V(X1,X3) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7361.0.1']),
% 36.18/36.60 [weight('<129,7360,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.7361.1.1',plain,
% 36.18/36.60 ( big_V(X3,big_hat(big_V(X1,X3),big_V(X1,X2))) = big_V(X1,X3) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7361.1.0','0.4793.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','R')]).
% 36.18/36.60 cnf('0.7361.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(big_V(X2,X1),big_V(X2,X3))) = big_V(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7361.1.1',theory(equality)]),
% 36.18/36.60 [u,rule_7339]).
% 36.18/36.60 cnf('0.7368.0.0',plain,
% 36.18/36.60 ( big_V(X1,X2) = big_V(X2,big_hat(big_V(X1,X3),big_V(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.7361.2.0','0.28.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.7368.1.0',plain,
% 36.18/36.60 ( big_V(X1,X2) = big_V(X2,big_hat(big_V(X1,X3),big_V(X1,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7368.0.0']),
% 36.18/36.60 [weight('<129,7361,28,[1,0,0,2]>')]).
% 36.18/36.60 cnf('0.7368.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(big_V(X2,X3),big_V(X2,X1))) = big_V(X2,X1) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7368.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7346]).
% 36.18/36.60 cnf('0.7522.0.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = implies(implies(X1,X2),big_hat(X2,big_V(X1,X3))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.4751.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.7522.1.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = implies(implies(X1,X2),big_hat(X2,big_V(X1,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7522.0.0']),
% 36.18/36.60 [weight('<169,4751,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.7522.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),big_hat(X2,big_V(X1,X3))) = big_V(X1,big_hat(X2,big_V(X1,X3))) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7522.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7496]).
% 36.18/36.60 cnf('0.7524.0.0',plain,
% 36.18/36.60 ( big_hat(X1,implies(implies(X2,X3),X3)) = big_hat(X1,big_V(X2,big_hat(X3,big_V(X2,X1)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5321.2.0','0.7522.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.7524.0.1',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,X3)) = big_hat(X1,big_V(X2,big_hat(X3,big_V(X2,X1)))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7524.0.0','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.7524.1.0',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,X3)) = big_hat(X1,big_V(X2,big_hat(X3,big_V(X2,X1)))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7524.0.1']),
% 36.18/36.60 [weight('<149,7522,5321,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.7524.2.0',plain,
% 36.18/36.60 ( big_hat(X1,big_V(X2,big_hat(X3,big_V(X2,X1)))) = big_hat(X1,big_V(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7524.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7498]).
% 36.18/36.60 cnf('0.7525.0.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,big_V(X1,X3)))) = big_V(big_hat(X2,big_V(X1,big_V(X1,X3))),big_hat(big_V(X1,X3),big_V(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.7368.2.0','0.7524.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.7525.0.1',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = big_V(big_hat(X2,big_V(X1,big_V(X1,X3))),big_hat(big_V(X1,X3),big_V(X1,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7525.0.0','0.29.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.7525.0.2',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = big_V(big_hat(X2,big_V(X1,X3)),big_hat(big_V(X1,X3),big_V(X1,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7525.0.1','0.29.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1.2','L')]).
% 36.18/36.60 cnf('0.7525.0.3',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = big_hat(big_V(X1,X3),big_V(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7525.0.2','0.2249.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.7525.1.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = big_hat(big_V(X1,X3),big_V(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7525.0.3']),
% 36.18/36.60 [weight('<119,7524,7368,[0,0,0,2]>')]).
% 36.18/36.60 cnf('0.7525.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,big_V(X1,X3))) = big_hat(big_V(X1,X3),big_V(X1,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7525.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_7499]).
% 36.18/36.60 cnf('0.7528.0.0',plain,
% 36.18/36.60 ( big_hat(big_V(X1,implies(X2,X1)),big_V(X1,X3)) = big_V(X1,big_hat(X3,implies(X2,X1))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.7525.2.0','0.31.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.7528.0.1',plain,
% 36.18/36.60 ( big_hat(implies(X2,X1),big_V(X1,X3)) = big_V(X1,big_hat(X3,implies(X2,X1))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.7528.0.0','0.31.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.7528.1.0',plain,
% 36.18/36.60 ( big_hat(implies(X2,X1),big_V(X1,X3)) = big_V(X1,big_hat(X3,implies(X2,X1))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.7528.0.1']),
% 36.18/36.60 [weight('<119,7525,31,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.7528.2.0',plain,
% 36.18/36.60 ( big_V(X1,big_hat(X2,implies(X3,X1))) = big_hat(implies(X3,X1),big_V(X1,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.7528.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_7502]).
% 36.18/36.60 cnf('0.8982.0.0',plain,
% 36.18/36.60 ( truth = implies(implies(implies(X1,X2),implies(X3,X2)),implies(big_V(X3,X2),big_V(X1,X2))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.210.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.8982.1.0',plain,
% 36.18/36.60 ( truth = implies(implies(implies(X1,X2),implies(X3,X2)),implies(big_V(X3,X2),big_V(X1,X2))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.8982.0.0']),
% 36.18/36.60 [weight('<?,210,5,[1,0,0,7]>')]).
% 36.18/36.60 cnf('0.8982.1.1',plain,
% 36.18/36.60 ( truth = implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,big_V(X1,X2))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8982.1.0','0.4733.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.8982.2.0',plain,
% 36.18/36.60 ( implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,big_V(X1,X2))) = truth ),
% 36.18/36.60 inference(orient,[status(thm)],['0.8982.1.1',theory(equality)]),
% 36.18/36.60 [x,rule_8930]).
% 36.18/36.60 cnf('0.8983.0.0',plain,
% 36.18/36.60 ( not(implies(X1,big_V(X2,X3))) = implies(big_V(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3))),not(truth)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.430.2.0','0.8982.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1','L')]).
% 36.18/36.60 cnf('0.8983.0.1',plain,
% 36.18/36.60 ( not(implies(X1,big_V(X2,X3))) = not(big_V(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3)))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8983.0.0','0.112.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.8983.0.2',plain,
% 36.18/36.60 ( not(implies(X1,big_V(X2,X3))) = not(implies(implies(X2,X3),implies(X1,X3))) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8983.0.1','0.2352.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.1','L')]).
% 36.18/36.60 cnf('0.8983.1.0',plain,
% 36.18/36.60 ( not(implies(X1,big_V(X2,X3))) = not(implies(implies(X2,X3),implies(X1,X3))) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.8983.0.2']),
% 36.18/36.60 [weight('<134,8982,430,[0,0,0,5]>')]).
% 36.18/36.60 cnf('0.8983.2.0',plain,
% 36.18/36.60 ( not(implies(implies(X1,X2),implies(X3,X2))) = not(implies(X3,big_V(X1,X2))) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.8983.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_8931]).
% 36.18/36.60 cnf('0.8984.0.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(X3,X2)) = not(not(implies(X3,big_V(X1,X2)))) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.114.2.0','0.8983.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.8984.0.1',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(X3,X2)) = implies(X3,big_V(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8984.0.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.8984.1.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(X3,X2)) = implies(X3,big_V(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.8984.0.1']),
% 36.18/36.60 [weight('<103,8983,114,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.8984.2.0',plain,
% 36.18/36.60 ( implies(implies(X1,X2),implies(X3,X2)) = implies(X3,big_V(X1,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.8984.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_8932]).
% 36.18/36.60 cnf('0.8985.0.0',plain,
% 36.18/36.60 ( implies(X1,big_V(implies(X2,X3),X3)) = implies(big_V(X2,X3),implies(X1,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.8984.2.0','0.5.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.8985.0.1',plain,
% 36.18/36.60 ( implies(X1,big_V(implies(X2,X3),X3)) = implies(X2,implies(X1,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8985.0.0','0.4734.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.8985.1.0',plain,
% 36.18/36.60 ( implies(X1,big_V(implies(X2,X3),X3)) = implies(X2,implies(X1,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.8985.0.1']),
% 36.18/36.60 [weight('<103,8984,5,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.8985.1.1',plain,
% 36.18/36.60 ( implies(X1,big_V(X3,implies(X2,X3))) = implies(X2,implies(X1,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8985.1.0','0.19.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.8985.1.2',plain,
% 36.18/36.60 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.8985.1.1','0.31.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.8985.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.8985.1.2']),
% 36.18/36.60 [equation_53]).
% 36.18/36.60 cnf('0.9008.0.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),implies(X2,X3)) = implies(not(X1),implies(X2,X3)) ),
% 36.18/36.60 inference(interreduction_right,[status(thm)],['0.4870.2.0'])).
% 36.18/36.60 cnf('0.9008.1.0',plain,
% 36.18/36.60 ( implies(not(big_hat(X1,X2)),implies(X2,X3)) = implies(not(X1),implies(X2,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9008.0.0']),
% 36.18/36.60 [weight('<134,4870,8985,[0,0,0,0]>')]).
% 36.18/36.60 cnf('0.9008.1.1',plain,
% 36.18/36.60 ( implies(X2,implies(not(big_hat(X1,X2)),X3)) = implies(not(X1),implies(X2,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9008.1.0','0.8985.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.9008.1.2',plain,
% 36.18/36.60 ( implies(X2,implies(not(X3),X1)) = implies(not(X1),implies(X2,X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9008.1.1','0.5298.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.9008.2.0',plain,
% 36.18/36.60 ( implies(X1,implies(not(X2),X3)) = implies(not(X3),implies(X1,X2)) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.9008.1.2']),
% 36.18/36.60 [equation_54]).
% 36.18/36.60 cnf('0.9012.0.0',plain,
% 36.18/36.60 ( implies(X1,big_V(not(X2),X3)) = implies(implies(not(X3),X2),implies(X1,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.8984.2.0','0.422.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.9012.1.0',plain,
% 36.18/36.60 ( implies(X1,big_V(not(X2),X3)) = implies(implies(not(X3),X2),implies(X1,X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9012.0.0']),
% 36.18/36.60 [weight('<134,8984,422,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.9012.2.0',plain,
% 36.18/36.60 ( implies(implies(not(X1),X2),implies(X3,X1)) = implies(X3,big_V(not(X2),X1)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9012.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_8958]).
% 36.18/36.60 cnf('0.9017.0.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),implies(not(X2),X3)) = implies(not(X3),implies(X1,X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.9008.2.0','0.32.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2','L')]).
% 36.18/36.60 cnf('0.9017.1.0',plain,
% 36.18/36.60 ( implies(big_V(X1,X2),implies(not(X2),X3)) = implies(not(X3),implies(X1,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9017.0.0']),
% 36.18/36.60 [weight('<134,9008,32,[1,1,0,3]>')]).
% 36.18/36.60 cnf('0.9017.1.1',plain,
% 36.18/36.60 ( implies(not(X2),implies(big_V(X1,X2),X3)) = implies(not(X3),implies(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9017.1.0','0.8985.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.9017.1.2',plain,
% 36.18/36.60 ( implies(not(X2),implies(X1,X3)) = implies(not(X3),implies(X1,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9017.1.1','0.5304.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.9017.2.0',plain,
% 36.18/36.60 ( implies(not(X1),implies(X2,X3)) = implies(not(X3),implies(X2,X1)) ),
% 36.18/36.60 inference(activate,[status(thm)],['0.9017.1.2']),
% 36.18/36.60 [equation_55]).
% 36.18/36.60 cnf('0.9018.0.0',plain,
% 36.18/36.60 ( big_V(not(X1),implies(X2,X3)) = implies(implies(not(X3),implies(X2,X1)),implies(X2,X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.9017.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.9018.0.1',plain,
% 36.18/36.60 ( big_V(not(X1),implies(X2,X3)) = implies(X2,big_V(not(implies(X2,X1)),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9018.0.0','0.9012.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.9018.1.0',plain,
% 36.18/36.60 ( big_V(not(X1),implies(X2,X3)) = implies(X2,big_V(not(implies(X2,X1)),X3)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9018.0.1']),
% 36.18/36.60 [weight('<134,9017,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.9018.2.0',plain,
% 36.18/36.60 ( implies(X1,big_V(not(implies(X1,X2)),X3)) = big_V(not(X2),implies(X1,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9018.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_8963]).
% 36.18/36.60 cnf('0.9021.0.0',plain,
% 36.18/36.60 ( big_V(not(not(X1)),implies(not(X2),X3)) = implies(not(X2),big_V(not(implies(X1,X2)),X3)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.9018.2.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.1.1','L')]).
% 36.18/36.60 cnf('0.9021.0.1',plain,
% 36.18/36.60 ( big_V(X1,implies(not(X2),X3)) = implies(not(X2),big_V(not(implies(X1,X2)),X3)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9021.0.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.9021.0.2',plain,
% 36.18/36.60 ( big_V(X1,implies(not(X2),X3)) = implies(big_hat(implies(X1,X2),not(X3)),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9021.0.1','0.804.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.9021.1.0',plain,
% 36.18/36.60 ( big_V(X1,implies(not(X2),X3)) = implies(big_hat(implies(X1,X2),not(X3)),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9021.0.2']),
% 36.18/36.60 [weight('<134,9018,409,[1,0,0,4]>')]).
% 36.18/36.60 cnf('0.9021.2.0',plain,
% 36.18/36.60 ( implies(big_hat(implies(X1,X2),not(X3)),X2) = big_V(X1,implies(not(X2),X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9021.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_8966]).
% 36.18/36.60 cnf('0.9022.0.0',plain,
% 36.18/36.60 ( big_V(X1,implies(not(X2),not(X3))) = implies(big_hat(implies(X1,X2),X3),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.9021.2.0','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.2','L')]).
% 36.18/36.60 cnf('0.9022.0.1',plain,
% 36.18/36.60 ( big_V(X1,implies(X3,X2)) = implies(big_hat(implies(X1,X2),X3),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9022.0.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.9022.1.0',plain,
% 36.18/36.60 ( big_V(X1,implies(X3,X2)) = implies(big_hat(implies(X1,X2),X3),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9022.0.1']),
% 36.18/36.60 [weight('<103,9021,114,[1,0,0,5]>')]).
% 36.18/36.60 cnf('0.9022.2.0',plain,
% 36.18/36.60 ( implies(big_hat(implies(X1,X2),X3),X2) = big_V(X1,implies(X3,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9022.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_8967]).
% 36.18/36.60 cnf('0.9025.0.0',plain,
% 36.18/36.60 ( big_V(big_hat(implies(X1,X2),X3),X2) = implies(big_V(X1,implies(X3,X2)),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.5.2.0','0.9022.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.9025.1.0',plain,
% 36.18/36.60 ( big_V(big_hat(implies(X1,X2),X3),X2) = implies(big_V(X1,implies(X3,X2)),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9025.0.0']),
% 36.18/36.60 [weight('<119,9022,5,[0,0,0,1]>')]).
% 36.18/36.60 cnf('0.9025.1.1',plain,
% 36.18/36.60 ( big_V(X2,big_hat(X3,implies(X1,X2))) = implies(big_V(X1,implies(X3,X2)),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9025.1.0','0.4793.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','R')]).
% 36.18/36.60 cnf('0.9025.1.2',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),big_V(X2,X3)) = implies(big_V(X1,implies(X3,X2)),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9025.1.1','0.7528.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.9025.2.0',plain,
% 36.18/36.60 ( implies(big_V(X1,implies(X2,X3)),X3) = big_hat(implies(X1,X3),big_V(X3,X2)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9025.1.2',theory(equality)]),
% 36.18/36.60 [x,rule_8970]).
% 36.18/36.60 cnf('0.9032.0.0',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),big_V(X2,implies(not(X2),X3))) = implies(big_V(X1,big_V(not(X3),X2)),X2) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.9025.2.0','0.420.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1.2','L')]).
% 36.18/36.60 cnf('0.9032.0.1',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(not(X2),X3)) = implies(big_V(X1,big_V(not(X3),X2)),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9032.0.0','0.189.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2','L')]).
% 36.18/36.60 cnf('0.9032.0.2',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(not(X2),X3)) = implies(big_V(X1,not(X3)),X2) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9032.0.1','0.4744.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('0.9032.1.0',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(not(X2),X3)) = implies(big_V(X1,not(X3)),X2) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9032.0.2']),
% 36.18/36.60 [weight('<134,9025,420,[1,0,0,3]>')]).
% 36.18/36.60 cnf('0.9032.2.0',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(not(X2),X3)) = implies(big_V(X1,not(X3)),X2) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9032.1.0',theory(equality)]),
% 36.18/36.60 [u,rule_8977]).
% 36.18/36.60 cnf('0.9034.0.0',plain,
% 36.18/36.60 ( implies(big_V(not(X1),not(X2)),not(X3)) = big_hat(implies(X3,X1),implies(not(not(X3)),X2)) ),
% 36.18/36.60 inference(cp,[status(thm)],['0.9032.2.0','0.409.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.1','L')]).
% 36.18/36.60 cnf('0.9034.0.1',plain,
% 36.18/36.60 ( implies(X3,big_hat(X1,not(not(X2)))) = big_hat(implies(X3,X1),implies(not(not(X3)),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9034.0.0','0.803.2.0',theory(equality)]),
% 36.18/36.60 [pos('L','L')]).
% 36.18/36.60 cnf('0.9034.0.2',plain,
% 36.18/36.60 ( implies(X3,big_hat(X1,X2)) = big_hat(implies(X3,X1),implies(not(not(X3)),X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9034.0.1','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('L.2.2','L')]).
% 36.18/36.60 cnf('0.9034.0.3',plain,
% 36.18/36.60 ( implies(X3,big_hat(X1,X2)) = big_hat(implies(X3,X1),implies(X3,X2)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['0.9034.0.2','0.114.2.0',theory(equality)]),
% 36.18/36.60 [pos('R.2.1','L')]).
% 36.18/36.60 cnf('0.9034.1.0',plain,
% 36.18/36.60 ( implies(X3,big_hat(X1,X2)) = big_hat(implies(X3,X1),implies(X3,X2)) ),
% 36.18/36.60 inference(weigh,[status(thm)],['0.9034.0.3']),
% 36.18/36.60 [weight('<103,9032,409,[1,0,0,1]>')]).
% 36.18/36.60 cnf('0.9034.2.0',plain,
% 36.18/36.60 ( big_hat(implies(X1,X2),implies(X1,X3)) = implies(X1,big_hat(X2,X3)) ),
% 36.18/36.60 inference(orient,[status(thm)],['0.9034.1.0',theory(equality)]),
% 36.18/36.60 [x,rule_8979]).
% 36.18/36.60 cnf('1.0.0.0',conjecture,
% 36.18/36.60 ( implies(x,big_hat(y,z)) = big_hat(implies(x,y),implies(x,z)) ),
% 36.18/36.60 file('/tmp/WALDMEISTER_26554_n010',conjecture_1)).
% 36.18/36.60 cnf('1.0.0.1',plain,
% 36.18/36.60 ( implies(x,big_hat(y,z)) = implies(x,big_hat(y,z)) ),
% 36.18/36.60 inference(reduction,[status(thm)],['1.0.0.0','0.9034.2.0',theory(equality)]),
% 36.18/36.60 [pos('R','L')]).
% 36.18/36.60 cnf('1.0.0.2',plain,
% 36.18/36.60 ( $true ),
% 36.18/36.60 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 36.18/36.60 [conjecture_1]).
% 36.18/36.60
% 36.18/36.60 Proved Goals:
% 36.18/36.60 No. 1: implies(x,big_hat(y,z)) ?= big_hat(implies(x,y),implies(x,z)) joined, current: implies(x,big_hat(y,z)) = implies(x,big_hat(y,z))
% 36.18/36.60 1 goal was specified, which was proved.
% 36.18/36.60 % SZS output end CNFRefutation
% 36.18/36.60 #END OF PROOF
% 36.18/36.60
% 36.18/36.60 Problem WALDMEISTER_26554_n010
% 36.18/36.60 CPs.gen 24893216
% 36.18/36.60 CPs.reexp 0
% 36.18/36.60 Select 340302
% 36.18/36.60 R 8979
% 36.18/36.60 E 55
% 36.18/36.60 vsize 14.3M
% 36.18/36.60 rss 11.2M
% 36.18/36.60 process.time 35.635s
% 36.18/36.60 wallclock.time 35.643s
% 36.18/36.60 status S
% 36.18/36.60
% 36.18/36.60
% 36.18/36.60 Waldmeister states: Goal proved.
% 36.18/36.60 % SZS status Unsatisfiable
%------------------------------------------------------------------------------