%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL153-1 : 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 : n011.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 07:58:06 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 9 sgn 16 !; 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_185,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_185]) ).
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_186,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_187,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_186]) ).
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_187]) ).
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,
not(x) != xor(x,truth),
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_25,plain,
not(x) != xor(x,truth),
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_188,plain,
not(x) != implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth)))),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_189,plain,
not(x) != implies(not(not(implies(not(not(x)),not(falsehood)))),not(implies(not(not(not(x))),not(truth)))),
inference(paramod,[status(thm)],[c_24,c_188]) ).
cnf(c_190,plain,
not(x) != implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(not(not(x))),not(truth)))),
inference(paramod,[status(thm)],[c_9,c_189]) ).
cnf(c_191,plain,
not(x) != implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(not(not(x))),falsehood))),
inference(paramod,[status(thm)],[c_24,c_190]) ).
cnf(c_192,plain,
not(x) != implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(falsehood),not(not(x))))),
inference(paramod,[status(thm)],[c_9,c_191]) ).
cnf(c_193,plain,
not(x) != implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))),
inference(paramod,[status(thm)],[c_9,c_192]) ).
cnf(c_26,plain,
implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))) != not(x),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,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_194]) ).
cnf(c_28,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_195,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_39,plain,
implies(implies(not(A),falsehood),A) = truth,
inference(paramod,[status(thm)],[c_24,c_195]) ).
cnf(c_72,plain,
implies(implies(falsehood,not(A)),implies(A,truth)) = truth,
inference(paramod,[status(thm)],[c_24,c_4]) ).
cnf(c_196,plain,
implies(falsehood,A) = implies(not(A),truth),
inference(paramod,[status(thm)],[c_24,c_9]) ).
cnf(c_74,plain,
implies(not(A),truth) = implies(falsehood,A),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_197,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_27,c_1]) ).
cnf(c_198,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_197]) ).
cnf(c_79,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,plain,
implies(implies(falsehood,A),truth) = implies(implies(truth,not(A)),not(A)),
inference(paramod,[status(thm)],[c_74,c_3]) ).
cnf(c_200,plain,
implies(implies(falsehood,A),truth) = implies(not(A),not(A)),
inference(paramod,[status(thm)],[c_1,c_199]) ).
cnf(c_104,plain,
implies(implies(falsehood,A),truth) = truth,
inference(paramod,[status(thm)],[c_79,c_200]) ).
cnf(c_105,plain,
implies(implies(not(A),truth),A) = implies(implies(A,falsehood),falsehood),
inference(paramod,[status(thm)],[c_74,c_3]) ).
cnf(c_201,plain,
implies(not(A),implies(implies(falsehood,A),truth)) = truth,
inference(paramod,[status(thm)],[c_74,c_27]) ).
cnf(c_111,plain,
implies(not(A),truth) = truth,
inference(paramod,[status(thm)],[c_104,c_201]) ).
cnf(c_202,plain,
implies(falsehood,implies(implies(not(A),truth),A)) = truth,
inference(paramod,[status(thm)],[c_74,c_27]) ).
cnf(c_203,plain,
implies(falsehood,implies(truth,A)) = truth,
inference(paramod,[status(thm)],[c_111,c_202]) ).
cnf(c_112,plain,
implies(falsehood,A) = truth,
inference(paramod,[status(thm)],[c_1,c_203]) ).
cnf(c_204,plain,
implies(truth,A) = implies(implies(A,falsehood),falsehood),
inference(paramod,[status(thm)],[c_111,c_105]) ).
cnf(c_205,plain,
A = implies(implies(A,falsehood),falsehood),
inference(paramod,[status(thm)],[c_1,c_204]) ).
cnf(c_114,plain,
implies(implies(A,falsehood),falsehood) = A,
inference(copy,[status(thm)],[c_205]) ).
cnf(c_206,plain,
implies(truth,implies(A,truth)) = truth,
inference(paramod,[status(thm)],[c_112,c_72]) ).
cnf(c_122,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_1,c_206]) ).
cnf(c_207,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_122,c_28]) ).
cnf(c_123,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_207]) ).
cnf(c_129,plain,
implies(implies(not(falsehood),A),falsehood) = not(A),
inference(paramod,[status(thm)],[c_9,c_114]) ).
cnf(c_137,plain,
implies(A,implies(not(A),B)) = truth,
inference(paramod,[status(thm)],[c_9,c_123]) ).
cnf(c_208,plain,
implies(truth,A) = implies(implies(A,implies(not(A),falsehood)),implies(not(A),falsehood)),
inference(paramod,[status(thm)],[c_39,c_3]) ).
cnf(c_209,plain,
A = implies(implies(A,implies(not(A),falsehood)),implies(not(A),falsehood)),
inference(paramod,[status(thm)],[c_1,c_208]) ).
cnf(c_210,plain,
A = implies(truth,implies(not(A),falsehood)),
inference(paramod,[status(thm)],[c_137,c_209]) ).
cnf(c_211,plain,
A = implies(not(A),falsehood),
inference(paramod,[status(thm)],[c_1,c_210]) ).
cnf(c_166,plain,
implies(not(A),falsehood) = A,
inference(copy,[status(thm)],[c_211]) ).
cnf(c_212,plain,
truth = implies(implies(falsehood,not(falsehood)),not(falsehood)),
inference(paramod,[status(thm)],[c_39,c_3]) ).
cnf(c_213,plain,
truth = implies(truth,not(falsehood)),
inference(paramod,[status(thm)],[c_112,c_212]) ).
cnf(c_214,plain,
truth = not(falsehood),
inference(paramod,[status(thm)],[c_1,c_213]) ).
cnf(c_167,plain,
not(falsehood) = truth,
inference(copy,[status(thm)],[c_214]) ).
cnf(c_215,plain,
implies(implies(truth,A),falsehood) = not(A),
inference(paramod,[status(thm)],[c_167,c_129]) ).
cnf(c_172,plain,
implies(A,falsehood) = not(A),
inference(paramod,[status(thm)],[c_1,c_215]) ).
cnf(c_216,plain,
implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(falsehood)),not(x)))) != not(x),
inference(paramod,[status(thm)],[c_167,c_26]) ).
cnf(c_217,plain,
implies(not(not(not(not(x)))),not(implies(not(not(falsehood)),not(x)))) != not(x),
inference(paramod,[status(thm)],[c_1,c_216]) ).
cnf(c_218,plain,
implies(not(not(not(not(x)))),not(implies(not(truth),not(x)))) != not(x),
inference(paramod,[status(thm)],[c_167,c_217]) ).
cnf(c_219,plain,
implies(not(not(not(not(x)))),not(implies(falsehood,not(x)))) != not(x),
inference(paramod,[status(thm)],[c_24,c_218]) ).
cnf(c_220,plain,
implies(not(not(not(not(x)))),not(truth)) != not(x),
inference(paramod,[status(thm)],[c_112,c_219]) ).
cnf(c_221,plain,
implies(not(not(not(not(x)))),falsehood) != not(x),
inference(paramod,[status(thm)],[c_24,c_220]) ).
cnf(c_175,plain,
not(not(not(not(not(x))))) != not(x),
inference(paramod,[status(thm)],[c_172,c_221]) ).
cnf(c_176,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_172,c_166]) ).
cnf(c_222,plain,
not(not(not(x))) != not(x),
inference(paramod,[status(thm)],[c_176,c_175]) ).
cnf(c_223,plain,
not(x) != not(x),
inference(paramod,[status(thm)],[c_176,c_222]) ).
cnf(c_184,plain,
$false,
inference(copy,[status(thm)],[c_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:55:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3006143 was started by sandbox on n011,
% 0.08/0.35 % Fri Sep 25 21:55:58 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % Assigning unary symbol not kb_weight 0 and highest precedence (10).
% 0.12/0.40
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.40 % Length of proof is 35.
% 0.12/0.40 % Level of proof is 11.
% 0.12/0.40 % Maximum clause weight is 82.000.
% 0.12/0.40 % Given clauses 24.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------