%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL158-1 : 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 : n005.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 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 2 sgn 20 !; 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_401,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_401]) ).
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_commutativity,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = and(VAR_1,VAR_0),
file('theBenchmark.p',and_commutativity) ).
cnf(c_14,plain,
and(A,B) = and(B,A),
inference(clausify,[status(thm)],[and_commutativity]) ).
cnf(c_402,plain,
not(implies(not(not(A)),not(B))) = and(B,A),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_15,plain,
not(implies(not(not(A)),not(B))) = not(implies(not(not(B)),not(A))),
inference(paramod,[status(thm)],[c_11,c_402]) ).
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_403,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_404,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_403]) ).
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_404]) ).
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]) ).
cnf(c_25,plain,
falsehood = not(truth),
inference(copy,[status(thm)],[c_24]) ).
fof(prove_alternative_wajsberg_axiom,axiom,
and_star(xor(truth,x),x) != falsehood,
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_26,plain,
and_star(xor(truth,x),x) != falsehood,
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_405,plain,
and_star(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))),x) != falsehood,
inference(paramod,[status(thm)],[c_17,c_26]) ).
cnf(c_406,plain,
and_star(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth))))),x) != falsehood,
inference(paramod,[status(thm)],[c_9,c_405]) ).
cnf(c_407,plain,
not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth))))))),not(x))) != falsehood,
inference(paramod,[status(thm)],[c_21,c_406]) ).
cnf(c_408,plain,
not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth)))))))) != falsehood,
inference(paramod,[status(thm)],[c_9,c_407]) ).
cnf(c_27,plain,
not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_25,c_408]) ).
cnf(c_409,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_28,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_409]) ).
cnf(c_410,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_34,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_410]) ).
cnf(c_59,plain,
implies(implies(not(not(A)),B),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_411,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_412,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_411]) ).
cnf(c_107,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_412]) ).
cnf(c_118,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_107,c_34]) ).
cnf(c_131,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_118,c_28]) ).
cnf(c_413,plain,
implies(truth,implies(A,not(not(A)))) = truth,
inference(paramod,[status(thm)],[c_107,c_59]) ).
cnf(c_312,plain,
implies(A,not(not(A))) = truth,
inference(paramod,[status(thm)],[c_1,c_413]) ).
cnf(c_414,plain,
implies(truth,not(not(A))) = implies(implies(not(not(A)),A),A),
inference(paramod,[status(thm)],[c_312,c_3]) ).
cnf(c_415,plain,
not(not(A)) = implies(implies(not(not(A)),A),A),
inference(paramod,[status(thm)],[c_1,c_414]) ).
cnf(c_416,plain,
not(not(A)) = implies(implies(not(A),not(A)),A),
inference(paramod,[status(thm)],[c_9,c_415]) ).
cnf(c_417,plain,
not(not(A)) = implies(truth,A),
inference(paramod,[status(thm)],[c_107,c_416]) ).
cnf(c_322,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_1,c_417]) ).
cnf(c_418,plain,
not(implies(x,not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_322,c_27]) ).
cnf(c_419,plain,
not(implies(x,not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_322,c_418]) ).
cnf(c_420,plain,
not(implies(x,not(implies(not(not(implies(truth,x))),not(implies(not(not(x)),not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_322,c_419]) ).
cnf(c_421,plain,
not(implies(x,not(implies(not(not(x)),not(implies(not(not(x)),not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_1,c_420]) ).
cnf(c_422,plain,
not(implies(x,not(implies(x,not(implies(not(not(x)),not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_322,c_421]) ).
cnf(c_423,plain,
not(implies(x,not(implies(x,not(implies(x,not(not(truth)))))))) != not(truth),
inference(paramod,[status(thm)],[c_322,c_422]) ).
cnf(c_424,plain,
not(implies(x,not(implies(x,not(implies(x,truth)))))) != not(truth),
inference(paramod,[status(thm)],[c_322,c_423]) ).
cnf(c_329,plain,
not(implies(x,not(implies(x,not(truth))))) != not(truth),
inference(paramod,[status(thm)],[c_131,c_424]) ).
cnf(c_425,plain,
not(implies(A,not(B))) = not(implies(not(not(B)),not(A))),
inference(paramod,[status(thm)],[c_322,c_15]) ).
cnf(c_397,plain,
not(implies(A,not(B))) = not(implies(B,not(A))),
inference(paramod,[status(thm)],[c_322,c_425]) ).
cnf(c_426,plain,
not(implies(x,not(implies(truth,not(x))))) != not(truth),
inference(paramod,[status(thm)],[c_397,c_329]) ).
cnf(c_427,plain,
not(implies(x,not(not(x)))) != not(truth),
inference(paramod,[status(thm)],[c_1,c_426]) ).
cnf(c_428,plain,
not(implies(x,x)) != not(truth),
inference(paramod,[status(thm)],[c_322,c_427]) ).
cnf(c_429,plain,
not(truth) != not(truth),
inference(paramod,[status(thm)],[c_107,c_428]) ).
cnf(c_400,plain,
$false,
inference(copy,[status(thm)],[c_429]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 21:56:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 345708 was started by sandbox on n005,
% 0.10/0.36 % Fri Sep 25 21:56:18 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 30.
% 0.13/0.42 % Level of proof is 6.
% 0.13/0.42 % Maximum clause weight is 27.000.
% 0.13/0.42 % Given clauses 33.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------