%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:58:08 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.54s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 99
% Number of leaves : 11
% Syntax : Number of formulae : 152 ( 152 unt; 0 def)
% Number of atoms : 152 ( 151 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 95 ( 95 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 20 ( 5 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wajsberg_1,axiom,
! [VAR_0] : implies(truth,VAR_0) = VAR_0,
file('theBenchmark.p',wajsberg_1) ).
cnf(c_1,plain,
implies(truth,A) = A,
inference(clausify,[status(thm)],[wajsberg_1]) ).
fof(wajsberg_2,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))) = truth,
file('theBenchmark.p',wajsberg_2) ).
cnf(c_2,plain,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
inference(clausify,[status(thm)],[wajsberg_2]) ).
fof(wajsberg_3,axiom,
! [VAR_0,VAR_1] : implies(implies(VAR_0,VAR_1),VAR_1) = implies(implies(VAR_1,VAR_0),VAR_0),
file('theBenchmark.p',wajsberg_3) ).
cnf(c_3,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(clausify,[status(thm)],[wajsberg_3]) ).
fof(wajsberg_4,axiom,
! [VAR_0,VAR_1] : implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0)) = truth,
file('theBenchmark.p',wajsberg_4) ).
cnf(c_4,plain,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
inference(clausify,[status(thm)],[wajsberg_4]) ).
fof(or_definition,axiom,
! [VAR_0,VAR_1] : or(VAR_0,VAR_1) = implies(not(VAR_0),VAR_1),
file('theBenchmark.p',or_definition) ).
cnf(c_5,plain,
or(A,B) = implies(not(A),B),
inference(clausify,[status(thm)],[or_definition]) ).
fof(or_commutativity,axiom,
! [VAR_0,VAR_1] : or(VAR_0,VAR_1) = or(VAR_1,VAR_0),
file('theBenchmark.p',or_commutativity) ).
cnf(c_8,plain,
or(A,B) = or(B,A),
inference(clausify,[status(thm)],[or_commutativity]) ).
cnf(c_174,plain,
implies(not(A),B) = or(B,A),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_9,plain,
implies(not(A),B) = implies(not(B),A),
inference(paramod,[status(thm)],[c_5,c_174]) ).
fof(and_definition,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_definition) ).
cnf(c_10,plain,
and(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_definition]) ).
cnf(c_11,plain,
and(A,B) = not(implies(not(not(A)),not(B))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
fof(xor_definition,axiom,
! [VAR_0,VAR_1] : xor(VAR_0,VAR_1) = or(and(VAR_0,not(VAR_1)),and(not(VAR_0),VAR_1)),
file('theBenchmark.p',xor_definition) ).
cnf(c_16,plain,
xor(A,B) = or(and(A,not(B)),and(not(A),B)),
inference(clausify,[status(thm)],[xor_definition]) ).
cnf(c_175,plain,
xor(A,B) = or(not(implies(not(not(A)),not(not(B)))),and(not(A),B)),
inference(paramod,[status(thm)],[c_11,c_16]) ).
cnf(c_176,plain,
xor(A,B) = or(not(implies(not(not(A)),not(not(B)))),not(implies(not(not(not(A))),not(B)))),
inference(paramod,[status(thm)],[c_11,c_175]) ).
cnf(c_17,plain,
xor(A,B) = implies(not(not(implies(not(not(A)),not(not(B))))),not(implies(not(not(not(A))),not(B)))),
inference(paramod,[status(thm)],[c_5,c_176]) ).
fof(and_star_definition,axiom,
! [VAR_0,VAR_1] : and_star(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_star_definition) ).
cnf(c_20,plain,
and_star(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_star_definition]) ).
cnf(c_21,plain,
and_star(A,B) = not(implies(not(not(A)),not(B))),
inference(paramod,[status(thm)],[c_5,c_20]) ).
fof(false_definition,axiom,
not(truth) = falsehood,
file('theBenchmark.p',false_definition) ).
cnf(c_24,plain,
not(truth) = falsehood,
inference(clausify,[status(thm)],[false_definition]) ).
fof(prove_alternative_wajsberg_axiom,axiom,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_25,plain,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_177,plain,
and_star(xor(and_star(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_178,plain,
and_star(xor(and_star(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(not(truth))),not(x)))),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_24,c_177]) ).
cnf(c_179,plain,
and_star(xor(and_star(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_24,c_178]) ).
cnf(c_180,plain,
and_star(xor(not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))),not(y))),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_21,c_179]) ).
cnf(c_181,plain,
and_star(xor(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_9,c_180]) ).
cnf(c_182,plain,
and_star(implies(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))),not(truth)))),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_17,c_181]) ).
cnf(c_183,plain,
and_star(implies(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(falsehood)))),not(implies(not(not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))),not(truth)))),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_24,c_182]) ).
cnf(c_184,plain,
and_star(implies(not(not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))))),not(implies(not(not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))),not(truth)))),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_9,c_183]) ).
cnf(c_185,plain,
and_star(implies(not(not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))))),not(implies(not(not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))),falsehood))),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_24,c_184]) ).
cnf(c_186,plain,
and_star(implies(not(not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))))),not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_9,c_185]) ).
cnf(c_187,plain,
and_star(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))))),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_9,c_186]) ).
cnf(c_188,plain,
not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))))))),not(y))) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_21,c_187]) ).
cnf(c_189,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(paramod,[status(thm)],[c_9,c_188]) ).
cnf(c_190,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(xor(and_star(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))),x),truth),x),
inference(paramod,[status(thm)],[c_17,c_189]) ).
cnf(c_191,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(xor(and_star(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(not(truth))),not(y)))),x),truth),x),
inference(paramod,[status(thm)],[c_24,c_190]) ).
cnf(c_192,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(xor(and_star(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))),x),truth),x),
inference(paramod,[status(thm)],[c_24,c_191]) ).
cnf(c_193,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(xor(not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))),not(x))),truth),x),
inference(paramod,[status(thm)],[c_21,c_192]) ).
cnf(c_194,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(xor(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))),truth),x),
inference(paramod,[status(thm)],[c_9,c_193]) ).
cnf(c_195,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(implies(not(not(implies(not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))),not(truth)))),x),
inference(paramod,[status(thm)],[c_17,c_194]) ).
cnf(c_196,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(implies(not(not(implies(not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(falsehood)))),not(implies(not(not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))),not(truth)))),x),
inference(paramod,[status(thm)],[c_24,c_195]) ).
cnf(c_197,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(implies(not(not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))))),not(implies(not(not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))),not(truth)))),x),
inference(paramod,[status(thm)],[c_9,c_196]) ).
cnf(c_198,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(implies(not(not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))))),not(implies(not(not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))),falsehood))),x),
inference(paramod,[status(thm)],[c_24,c_197]) ).
cnf(c_199,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(implies(not(not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))))),not(implies(not(falsehood),not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),x),
inference(paramod,[status(thm)],[c_9,c_198]) ).
cnf(c_200,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != and_star(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))))),x),
inference(paramod,[status(thm)],[c_9,c_199]) ).
cnf(c_201,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))))))),not(x))),
inference(paramod,[status(thm)],[c_21,c_200]) ).
cnf(c_202,plain,
not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))) != not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))),
inference(paramod,[status(thm)],[c_9,c_201]) ).
cnf(c_26,plain,
not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_203,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_27,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_203]) ).
cnf(c_34,plain,
implies(implies(not(A),B),A) = implies(implies(A,not(B)),not(B)),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_35,plain,
implies(implies(not(not(A)),B),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_204,plain,
implies(falsehood,A) = implies(not(A),truth),
inference(paramod,[status(thm)],[c_24,c_9]) ).
cnf(c_43,plain,
implies(not(A),truth) = implies(falsehood,A),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_205,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_27,c_1]) ).
cnf(c_206,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_205]) ).
cnf(c_44,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
implies(implies(falsehood,A),truth) = implies(implies(truth,not(A)),not(A)),
inference(paramod,[status(thm)],[c_43,c_3]) ).
cnf(c_208,plain,
implies(implies(falsehood,A),truth) = implies(not(A),not(A)),
inference(paramod,[status(thm)],[c_1,c_207]) ).
cnf(c_57,plain,
implies(implies(falsehood,A),truth) = truth,
inference(paramod,[status(thm)],[c_44,c_208]) ).
cnf(c_209,plain,
implies(not(A),implies(implies(falsehood,A),truth)) = truth,
inference(paramod,[status(thm)],[c_43,c_27]) ).
cnf(c_210,plain,
implies(not(A),truth) = truth,
inference(paramod,[status(thm)],[c_57,c_209]) ).
cnf(c_60,plain,
implies(falsehood,A) = truth,
inference(paramod,[status(thm)],[c_43,c_210]) ).
cnf(c_211,plain,
implies(truth,A) = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_44,c_34]) ).
cnf(c_212,plain,
A = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_1,c_211]) ).
cnf(c_79,plain,
implies(implies(A,not(not(A))),not(not(A))) = A,
inference(copy,[status(thm)],[c_212]) ).
cnf(c_213,plain,
implies(truth,implies(A,not(not(A)))) = truth,
inference(paramod,[status(thm)],[c_44,c_35]) ).
cnf(c_83,plain,
implies(A,not(not(A))) = truth,
inference(paramod,[status(thm)],[c_1,c_213]) ).
cnf(c_214,plain,
implies(truth,not(not(A))) = A,
inference(paramod,[status(thm)],[c_83,c_79]) ).
cnf(c_85,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_1,c_214]) ).
cnf(c_215,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_26]) ).
cnf(c_216,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_215]) ).
cnf(c_217,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(not(not(implies(not(falsehood),y))),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_216]) ).
cnf(c_218,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(implies(not(falsehood),y),not(implies(not(not(falsehood)),not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_217]) ).
cnf(c_219,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(implies(not(falsehood),y),not(implies(falsehood,not(y)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_218]) ).
cnf(c_220,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(implies(not(falsehood),y),not(truth)))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_219]) ).
cnf(c_221,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(implies(not(falsehood),y),falsehood))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_24,c_220]) ).
cnf(c_222,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(implies(falsehood,not(y)),not(y)))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_34,c_221]) ).
cnf(c_223,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(implies(truth,not(y)))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_222]) ).
cnf(c_224,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,not(not(y))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_1,c_223]) ).
cnf(c_225,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(not(implies(x,y))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_224]) ).
cnf(c_226,plain,
not(implies(x,not(implies(not(not(implies(not(falsehood),not(implies(x,y))))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_225]) ).
cnf(c_227,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(not(not(falsehood)),not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_226]) ).
cnf(c_228,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_227]) ).
cnf(c_229,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_228]) ).
cnf(c_230,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(not(not(implies(not(falsehood),y))),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_229]) ).
cnf(c_231,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(implies(not(falsehood),y),not(implies(not(not(falsehood)),not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_230]) ).
cnf(c_232,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(implies(not(falsehood),y),not(implies(falsehood,not(y)))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_231]) ).
cnf(c_233,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(implies(not(falsehood),y),not(truth)))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_232]) ).
cnf(c_234,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(implies(not(falsehood),y),falsehood))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_24,c_233]) ).
cnf(c_235,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(implies(falsehood,not(y)),not(y)))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_34,c_234]) ).
cnf(c_236,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(implies(truth,not(y)))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_235]) ).
cnf(c_237,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,not(not(y))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_1,c_236]) ).
cnf(c_238,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,not(not(implies(x,y))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_237]) ).
cnf(c_239,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(implies(falsehood,implies(x,y))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_238]) ).
cnf(c_240,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),not(truth))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_239]) ).
cnf(c_241,plain,
not(implies(x,not(implies(implies(not(falsehood),not(implies(x,y))),falsehood)))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_24,c_240]) ).
cnf(c_242,plain,
not(implies(x,not(implies(implies(falsehood,not(not(implies(x,y)))),not(not(implies(x,y))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_34,c_241]) ).
cnf(c_243,plain,
not(implies(x,not(implies(implies(falsehood,implies(x,y)),not(not(implies(x,y))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_242]) ).
cnf(c_244,plain,
not(implies(x,not(implies(truth,not(not(implies(x,y))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_243]) ).
cnf(c_245,plain,
not(implies(x,not(implies(truth,implies(x,y))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_244]) ).
cnf(c_246,plain,
not(implies(x,not(implies(x,y)))) != not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_1,c_245]) ).
cnf(c_247,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_246]) ).
cnf(c_248,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_247]) ).
cnf(c_249,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(not(not(implies(not(falsehood),x))),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_248]) ).
cnf(c_250,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(implies(not(falsehood),x),not(implies(not(not(falsehood)),not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_249]) ).
cnf(c_251,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(implies(not(falsehood),x),not(implies(falsehood,not(x)))))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_250]) ).
cnf(c_252,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(implies(not(falsehood),x),not(truth)))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_251]) ).
cnf(c_253,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(implies(not(falsehood),x),falsehood))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_24,c_252]) ).
cnf(c_254,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(implies(falsehood,not(x)),not(x)))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_34,c_253]) ).
cnf(c_255,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(implies(truth,not(x)))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_60,c_254]) ).
cnf(c_256,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,not(not(x))))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_1,c_255]) ).
cnf(c_257,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(not(implies(y,x))))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_256]) ).
cnf(c_258,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(not(not(implies(not(falsehood),not(implies(y,x))))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_257]) ).
cnf(c_259,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(not(not(falsehood)),not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_258]) ).
cnf(c_260,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(not(not(y)),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_259]) ).
cnf(c_261,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_260]) ).
cnf(c_262,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(not(not(implies(not(falsehood),x))),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_261]) ).
cnf(c_263,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(implies(not(falsehood),x),not(implies(not(not(falsehood)),not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_262]) ).
cnf(c_264,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(implies(not(falsehood),x),not(implies(falsehood,not(x)))))))))))))),
inference(paramod,[status(thm)],[c_85,c_263]) ).
cnf(c_265,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(implies(not(falsehood),x),not(truth)))))))))))),
inference(paramod,[status(thm)],[c_60,c_264]) ).
cnf(c_266,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(implies(not(falsehood),x),falsehood))))))))))),
inference(paramod,[status(thm)],[c_24,c_265]) ).
cnf(c_267,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(implies(falsehood,not(x)),not(x)))))))))))),
inference(paramod,[status(thm)],[c_34,c_266]) ).
cnf(c_268,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(implies(truth,not(x)))))))))))),
inference(paramod,[status(thm)],[c_60,c_267]) ).
cnf(c_269,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,not(not(x))))))))))),
inference(paramod,[status(thm)],[c_1,c_268]) ).
cnf(c_270,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,not(not(implies(y,x))))))))),
inference(paramod,[status(thm)],[c_85,c_269]) ).
cnf(c_271,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(implies(falsehood,implies(y,x))))))),
inference(paramod,[status(thm)],[c_85,c_270]) ).
cnf(c_272,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),not(truth))))),
inference(paramod,[status(thm)],[c_60,c_271]) ).
cnf(c_273,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(not(falsehood),not(implies(y,x))),falsehood)))),
inference(paramod,[status(thm)],[c_24,c_272]) ).
cnf(c_274,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(falsehood,not(not(implies(y,x)))),not(not(implies(y,x))))))),
inference(paramod,[status(thm)],[c_34,c_273]) ).
cnf(c_275,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(implies(falsehood,implies(y,x)),not(not(implies(y,x))))))),
inference(paramod,[status(thm)],[c_85,c_274]) ).
cnf(c_276,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(truth,not(not(implies(y,x))))))),
inference(paramod,[status(thm)],[c_60,c_275]) ).
cnf(c_277,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(truth,implies(y,x))))),
inference(paramod,[status(thm)],[c_85,c_276]) ).
cnf(c_278,plain,
not(implies(x,not(implies(x,y)))) != not(implies(y,not(implies(y,x)))),
inference(paramod,[status(thm)],[c_1,c_277]) ).
cnf(c_86,plain,
not(implies(y,not(implies(y,x)))) != not(implies(x,not(implies(x,y)))),
inference(copy,[status(thm)],[c_278]) ).
cnf(c_279,plain,
implies(A,B) = implies(not(B),not(A)),
inference(paramod,[status(thm)],[c_85,c_9]) ).
cnf(c_94,plain,
implies(not(A),not(B)) = implies(B,A),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_280,plain,
implies(implies(not(not(A)),B),not(A)) = implies(implies(B,A),not(B)),
inference(paramod,[status(thm)],[c_94,c_34]) ).
cnf(c_108,plain,
implies(implies(A,B),not(A)) = implies(implies(B,A),not(B)),
inference(paramod,[status(thm)],[c_85,c_280]) ).
cnf(c_112,plain,
implies(A,not(B)) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_85,c_94]) ).
cnf(c_281,plain,
implies(A,not(implies(A,B))) = implies(implies(B,A),not(B)),
inference(paramod,[status(thm)],[c_112,c_108]) ).
cnf(c_118,plain,
implies(A,not(implies(A,B))) = implies(B,not(implies(B,A))),
inference(paramod,[status(thm)],[c_112,c_281]) ).
cnf(c_282,plain,
not(implies(x,not(implies(x,y)))) != not(implies(x,not(implies(x,y)))),
inference(paramod,[status(thm)],[c_118,c_86]) ).
cnf(c_173,plain,
$false,
inference(copy,[status(thm)],[c_282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 21:56:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1789850 was started by sandbox on n010,
% 0.12/0.36 % Fri Sep 25 21:56:31 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.54/0.54
% 0.54/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.54/0.54
% 0.54/0.54 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.54/0.54 % Length of proof is 32.
% 0.54/0.54 % Level of proof is 8.
% 0.54/0.54 % Maximum clause weight is 223.000.
% 0.54/0.54 % Given clauses 42.
% 0.54/0.54
% 0.54/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------