%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:58:07 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 11
% Syntax : Number of formulae : 132 ( 132 unt; 0 def)
% Number of atoms : 132 ( 131 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 60 ( 60 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 118 ( 10 sgn 19 !; 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_209,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_209]) ).
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(and_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : and(and(VAR_0,VAR_1),VAR_2) = and(VAR_0,and(VAR_1,VAR_2)),
file('theBenchmark.p',and_associativity) ).
cnf(c_12,plain,
and(and(A,B),C) = and(A,and(B,C)),
inference(clausify,[status(thm)],[and_associativity]) ).
cnf(c_210,plain,
and(not(implies(not(not(A)),not(B))),C) = and(A,and(B,C)),
inference(paramod,[status(thm)],[c_11,c_12]) ).
cnf(c_211,plain,
not(implies(not(not(not(implies(not(not(A)),not(B))))),not(C))) = and(A,and(B,C)),
inference(paramod,[status(thm)],[c_11,c_210]) ).
cnf(c_212,plain,
not(implies(not(not(not(implies(not(not(A)),not(B))))),not(C))) = and(A,not(implies(not(not(B)),not(C)))),
inference(paramod,[status(thm)],[c_11,c_211]) ).
cnf(c_13,plain,
not(implies(not(not(not(implies(not(not(A)),not(B))))),not(C))) = not(implies(not(not(A)),not(not(implies(not(not(B)),not(C)))))),
inference(paramod,[status(thm)],[c_11,c_212]) ).
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_213,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_214,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_213]) ).
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_214]) ).
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,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_25,plain,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_215,plain,
xor(x,implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))) != xor(xor(x,truth),y),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_216,plain,
xor(x,implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(not(truth))),not(y))))) != xor(xor(x,truth),y),
inference(paramod,[status(thm)],[c_24,c_215]) ).
cnf(c_217,plain,
xor(x,implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))) != xor(xor(x,truth),y),
inference(paramod,[status(thm)],[c_24,c_216]) ).
cnf(c_218,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(xor(x,truth),y),
inference(paramod,[status(thm)],[c_17,c_217]) ).
cnf(c_219,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth)))),y),
inference(paramod,[status(thm)],[c_17,c_218]) ).
cnf(c_220,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(implies(not(not(implies(not(not(x)),not(falsehood)))),not(implies(not(not(not(x))),not(truth)))),y),
inference(paramod,[status(thm)],[c_24,c_219]) ).
cnf(c_221,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(not(not(x))),not(truth)))),y),
inference(paramod,[status(thm)],[c_9,c_220]) ).
cnf(c_222,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(not(not(x))),falsehood))),y),
inference(paramod,[status(thm)],[c_24,c_221]) ).
cnf(c_223,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(falsehood),not(not(x))))),y),
inference(paramod,[status(thm)],[c_9,c_222]) ).
cnf(c_224,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != xor(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))),y),
inference(paramod,[status(thm)],[c_9,c_223]) ).
cnf(c_225,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))),not(not(y))))),not(implies(not(not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))),not(y)))),
inference(paramod,[status(thm)],[c_17,c_224]) ).
cnf(c_226,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(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(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))),not(y)))),
inference(paramod,[status(thm)],[c_9,c_225]) ).
cnf(c_227,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))),not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),
inference(paramod,[status(thm)],[c_9,c_226]) ).
cnf(c_26,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_9,c_227]) ).
cnf(c_228,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_228]) ).
cnf(c_28,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_229,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_33,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_230,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_40,plain,
implies(implies(not(A),falsehood),A) = truth,
inference(paramod,[status(thm)],[c_24,c_230]) ).
cnf(c_57,plain,
implies(implies(not(A),B),A) = implies(implies(A,not(B)),not(B)),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_63,plain,
implies(implies(A,not(falsehood)),not(falsehood)) = truth,
inference(paramod,[status(thm)],[c_57,c_40]) ).
cnf(c_231,plain,
implies(falsehood,A) = implies(not(A),truth),
inference(paramod,[status(thm)],[c_24,c_9]) ).
cnf(c_108,plain,
implies(not(A),truth) = implies(falsehood,A),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_232,plain,
not(implies(not(not(not(implies(not(falsehood),not(A))))),not(B))) = not(implies(not(not(truth)),not(not(implies(not(not(A)),not(B)))))),
inference(paramod,[status(thm)],[c_24,c_13]) ).
cnf(c_109,plain,
not(implies(not(not(not(implies(not(falsehood),not(A))))),not(B))) = not(implies(not(falsehood),not(not(implies(not(not(A)),not(B)))))),
inference(paramod,[status(thm)],[c_24,c_232]) ).
cnf(c_233,plain,
not(implies(not(not(not(implies(not(not(A)),falsehood)))),not(B))) = not(implies(not(not(A)),not(not(implies(not(not(truth)),not(B)))))),
inference(paramod,[status(thm)],[c_24,c_13]) ).
cnf(c_234,plain,
not(implies(not(not(not(implies(not(falsehood),not(A))))),not(B))) = not(implies(not(not(A)),not(not(implies(not(not(truth)),not(B)))))),
inference(paramod,[status(thm)],[c_9,c_233]) ).
cnf(c_235,plain,
not(implies(not(falsehood),not(not(implies(not(not(A)),not(B)))))) = not(implies(not(not(A)),not(not(implies(not(not(truth)),not(B)))))),
inference(paramod,[status(thm)],[c_109,c_234]) ).
cnf(c_236,plain,
not(implies(not(falsehood),not(not(implies(not(not(A)),not(B)))))) = not(implies(not(not(A)),not(not(implies(not(falsehood),not(B)))))),
inference(paramod,[status(thm)],[c_24,c_235]) ).
cnf(c_110,plain,
not(implies(not(not(A)),not(not(implies(not(falsehood),not(B)))))) = not(implies(not(falsehood),not(not(implies(not(not(A)),not(B)))))),
inference(copy,[status(thm)],[c_236]) ).
cnf(c_237,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_27,c_1]) ).
cnf(c_238,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_237]) ).
cnf(c_112,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_238]) ).
cnf(c_123,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_112,c_33]) ).
cnf(c_138,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_123,c_27]) ).
cnf(c_239,plain,
truth = implies(falsehood,A),
inference(paramod,[status(thm)],[c_138,c_108]) ).
cnf(c_139,plain,
implies(falsehood,A) = truth,
inference(copy,[status(thm)],[c_239]) ).
cnf(c_240,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_138,c_28]) ).
cnf(c_140,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_240]) ).
cnf(c_241,plain,
implies(truth,not(falsehood)) = implies(implies(not(falsehood),implies(A,not(falsehood))),implies(A,not(falsehood))),
inference(paramod,[status(thm)],[c_63,c_3]) ).
cnf(c_242,plain,
not(falsehood) = implies(implies(not(falsehood),implies(A,not(falsehood))),implies(A,not(falsehood))),
inference(paramod,[status(thm)],[c_1,c_241]) ).
cnf(c_243,plain,
not(falsehood) = implies(truth,implies(A,not(falsehood))),
inference(paramod,[status(thm)],[c_140,c_242]) ).
cnf(c_244,plain,
not(falsehood) = implies(A,not(falsehood)),
inference(paramod,[status(thm)],[c_1,c_243]) ).
cnf(c_200,plain,
implies(A,not(falsehood)) = not(falsehood),
inference(copy,[status(thm)],[c_244]) ).
cnf(c_245,plain,
truth = implies(implies(not(falsehood),A),A),
inference(paramod,[status(thm)],[c_63,c_3]) ).
cnf(c_201,plain,
implies(implies(not(falsehood),A),A) = truth,
inference(copy,[status(thm)],[c_245]) ).
cnf(c_246,plain,
implies(implies(implies(not(falsehood),A),A),not(falsehood)) = truth,
inference(paramod,[status(thm)],[c_3,c_63]) ).
cnf(c_247,plain,
implies(truth,not(falsehood)) = truth,
inference(paramod,[status(thm)],[c_201,c_246]) ).
cnf(c_202,plain,
not(falsehood) = truth,
inference(paramod,[status(thm)],[c_200,c_247]) ).
cnf(c_248,plain,
not(implies(not(not(A)),not(not(implies(truth,not(B)))))) = not(implies(not(falsehood),not(not(implies(not(not(A)),not(B)))))),
inference(paramod,[status(thm)],[c_202,c_110]) ).
cnf(c_249,plain,
not(implies(not(not(A)),not(not(not(B))))) = not(implies(not(falsehood),not(not(implies(not(not(A)),not(B)))))),
inference(paramod,[status(thm)],[c_1,c_248]) ).
cnf(c_250,plain,
not(implies(not(not(A)),not(not(not(B))))) = not(implies(truth,not(not(implies(not(not(A)),not(B)))))),
inference(paramod,[status(thm)],[c_202,c_249]) ).
cnf(c_206,plain,
not(implies(not(not(A)),not(not(not(B))))) = not(not(not(implies(not(not(A)),not(B))))),
inference(paramod,[status(thm)],[c_1,c_250]) ).
cnf(c_251,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_26]) ).
cnf(c_252,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_251]) ).
cnf(c_253,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(not(truth),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_252]) ).
cnf(c_254,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_253]) ).
cnf(c_255,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(truth))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_139,c_254]) ).
cnf(c_256,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),falsehood)))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_255]) ).
cnf(c_257,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(falsehood),not(not(not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_9,c_256]) ).
cnf(c_258,plain,
implies(not(not(implies(not(not(x)),not(not(implies(truth,not(not(not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_257]) ).
cnf(c_259,plain,
implies(not(not(implies(not(not(x)),not(not(not(not(not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_258]) ).
cnf(c_260,plain,
implies(not(not(not(not(implies(not(not(x)),not(not(not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_206,c_259]) ).
cnf(c_261,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_206,c_260]) ).
cnf(c_262,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_261]) ).
cnf(c_263,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_262]) ).
cnf(c_264,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(not(truth),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_263]) ).
cnf(c_265,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_264]) ).
cnf(c_266,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(truth)))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_139,c_265]) ).
cnf(c_267,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),falsehood))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_266]) ).
cnf(c_268,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(not(falsehood),not(not(not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_9,c_267]) ).
cnf(c_269,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(implies(truth,not(not(not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_268]) ).
cnf(c_270,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(x))),not(not(not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_269]) ).
cnf(c_271,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_206,c_270]) ).
cnf(c_272,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_202,c_271]) ).
cnf(c_273,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(implies(not(not(falsehood)),not(x))))))))),not(implies(not(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_272]) ).
cnf(c_274,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(implies(not(truth),not(x))))))))),not(implies(not(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_202,c_273]) ).
cnf(c_275,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x))))))))),not(implies(not(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_274]) ).
cnf(c_276,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(truth))))))),not(implies(not(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_139,c_275]) ).
cnf(c_277,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),falsehood)))))),not(implies(not(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_276]) ).
cnf(c_278,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(falsehood),not(not(not(x))))))))),not(implies(not(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_9,c_277]) ).
cnf(c_279,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(implies(truth,not(not(not(x))))))))),not(implies(not(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_202,c_278]) ).
cnf(c_280,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(implies(not(not(y)),not(not(not(not(not(x)))))))),not(implies(not(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_279]) ).
cnf(c_281,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(not(x)))))))),not(implies(not(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_206,c_280]) ).
cnf(c_282,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(y)),not(x)))))))),not(implies(not(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_206,c_281]) ).
cnf(c_283,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(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_9,c_282]) ).
cnf(c_284,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(falsehood)),not(x)))))))),
inference(paramod,[status(thm)],[c_202,c_283]) ).
cnf(c_285,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(implies(not(not(falsehood)),not(x)))))))),
inference(paramod,[status(thm)],[c_1,c_284]) ).
cnf(c_286,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(implies(not(truth),not(x)))))))),
inference(paramod,[status(thm)],[c_202,c_285]) ).
cnf(c_287,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x)))))))),
inference(paramod,[status(thm)],[c_24,c_286]) ).
cnf(c_288,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(truth)))))),
inference(paramod,[status(thm)],[c_139,c_287]) ).
cnf(c_289,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),falsehood))))),
inference(paramod,[status(thm)],[c_24,c_288]) ).
cnf(c_290,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(not(falsehood),not(not(not(x)))))))),
inference(paramod,[status(thm)],[c_9,c_289]) ).
cnf(c_291,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(implies(truth,not(not(not(x)))))))),
inference(paramod,[status(thm)],[c_202,c_290]) ).
cnf(c_292,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(implies(not(not(not(y))),not(not(not(not(x))))))),
inference(paramod,[status(thm)],[c_1,c_291]) ).
cnf(c_293,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(y))),not(not(x))))))),
inference(paramod,[status(thm)],[c_206,c_292]) ).
cnf(c_294,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(paramod,[status(thm)],[c_9,c_293]) ).
cnf(c_208,plain,
$false,
inference(copy,[status(thm)],[c_294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n018.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 21:58:36 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.58 % Process 2939091 was started by sandbox2 on n018,
% 0.10/0.58 % Fri Sep 25 21:58:36 2026
% 0.10/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.58
% 0.10/0.58 % From the command line: assign(max_seconds, 300).
% 0.15/0.64
% 0.15/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.64
% 0.15/0.64 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.64 % Length of proof is 35.
% 0.15/0.64 % Level of proof is 9.
% 0.15/0.64 % Maximum clause weight is 97.000.
% 0.15/0.64 % Given clauses 25.
% 0.15/0.64
% 0.15/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------