%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL115-2 : 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 : n017.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 07:58:02 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 10 sgn 8 !; 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(prove_mv_39,axiom,
implies(not(implies(a,b)),not(b)) != truth,
file('theBenchmark.p',prove_mv_39) ).
cnf(c_5,plain,
implies(not(implies(a,b)),not(b)) != truth,
inference(clausify,[status(thm)],[prove_mv_39]) ).
cnf(c_191,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_191]) ).
cnf(c_7,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_192,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_12,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_194,plain,
implies(implies(implies(A,B),B),A) = implies(implies(implies(B,A),A),A),
inference(paramod,[status(thm)],[c_3,c_193]) ).
cnf(c_17,plain,
implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_18,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_195,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_196,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_195]) ).
cnf(c_27,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_196]) ).
cnf(c_35,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_27,c_12]) ).
cnf(c_41,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_35,c_6]) ).
cnf(c_197,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_41,c_7]) ).
cnf(c_42,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_197]) ).
cnf(c_198,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_42,c_2]) ).
cnf(c_43,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_198]) ).
cnf(c_199,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_200,plain,
implies(A,B) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_1,c_199]) ).
cnf(c_45,plain,
implies(implies(implies(A,B),B),B) = implies(A,B),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,plain,
implies(A,B) = implies(implies(implies(B,A),A),B),
inference(paramod,[status(thm)],[c_45,c_17]) ).
cnf(c_46,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_18,c_46]) ).
cnf(c_203,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_1,c_202]) ).
cnf(c_85,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_204,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_18,c_43]) ).
cnf(c_102,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_1,c_204]) ).
cnf(c_205,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_102,c_85]) ).
cnf(c_110,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_205]) ).
cnf(c_206,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_102,c_3]) ).
cnf(c_207,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_206]) ).
cnf(c_112,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_207]) ).
cnf(c_208,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_112,c_4]) ).
cnf(c_209,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_110,c_208]) ).
cnf(c_151,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_209]) ).
cnf(c_210,plain,
implies(truth,implies(A,implies(not(A),not(truth)))) = truth,
inference(paramod,[status(thm)],[c_151,c_4]) ).
cnf(c_162,plain,
implies(A,implies(not(A),not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_210]) ).
cnf(c_211,plain,
implies(truth,implies(not(A),not(truth))) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_162,c_3]) ).
cnf(c_212,plain,
implies(not(A),not(truth)) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_1,c_211]) ).
cnf(c_213,plain,
implies(not(A),not(truth)) = implies(truth,A),
inference(paramod,[status(thm)],[c_18,c_212]) ).
cnf(c_168,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_213]) ).
cnf(c_214,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_168,c_3]) ).
cnf(c_215,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_102,c_214]) ).
cnf(c_172,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_1,c_215]) ).
cnf(c_216,plain,
implies(not(implies(A,B)),implies(B,not(truth))) = truth,
inference(paramod,[status(thm)],[c_172,c_43]) ).
cnf(c_189,plain,
implies(not(implies(A,B)),not(B)) = truth,
inference(paramod,[status(thm)],[c_172,c_216]) ).
cnf(c_190,plain,
$false,
inference(resolve,[status(thm)],[c_189,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL115-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n017.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 21:48:03 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 3280813 was started by sandbox on n017,
% 0.20/0.46 % Fri Sep 25 21:48:03 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.20/0.52
% 0.20/0.52 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 0.20/0.52
% 0.20/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.52
% 0.20/0.52 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.20/0.52 % Length of proof is 27.
% 0.20/0.52 % Level of proof is 15.
% 0.20/0.52 % Maximum clause weight is 55.000.
% 0.20/0.52 % Given clauses 26.
% 0.20/0.52
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------