%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL116-2 : 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 : 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 07:58:02 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 93 ( 8 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_50,axiom,
implies(not(a),implies(b,not(implies(b,a)))) != truth,
file('theBenchmark.p',prove_mv_50) ).
cnf(c_5,plain,
implies(not(a),implies(b,not(implies(b,a)))) != truth,
inference(clausify,[status(thm)],[prove_mv_50]) ).
cnf(c_218,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_218]) ).
cnf(c_7,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_219,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_219]) ).
cnf(c_220,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_221,plain,
implies(implies(implies(A,B),B),A) = implies(implies(implies(B,A),A),A),
inference(paramod,[status(thm)],[c_3,c_220]) ).
cnf(c_17,plain,
implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_18,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_222,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_223,plain,
implies(A,B) = implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))),
inference(paramod,[status(thm)],[c_1,c_222]) ).
cnf(c_24,plain,
implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B),
inference(copy,[status(thm)],[c_223]) ).
cnf(c_224,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_225,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_224]) ).
cnf(c_27,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_225]) ).
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_226,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_226]) ).
cnf(c_227,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_227]) ).
cnf(c_228,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_229,plain,
implies(A,B) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_1,c_228]) ).
cnf(c_45,plain,
implies(implies(implies(A,B),B),B) = implies(A,B),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_230,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_230]) ).
cnf(c_231,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_18,c_46]) ).
cnf(c_232,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_1,c_231]) ).
cnf(c_85,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_232]) ).
cnf(c_233,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_233]) ).
cnf(c_234,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_234]) ).
cnf(c_235,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_102,c_3]) ).
cnf(c_236,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_235]) ).
cnf(c_112,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_236]) ).
cnf(c_237,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_112,c_4]) ).
cnf(c_238,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_110,c_237]) ).
cnf(c_151,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_238]) ).
cnf(c_239,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_239]) ).
cnf(c_240,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_241,plain,
implies(not(A),not(truth)) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_1,c_240]) ).
cnf(c_242,plain,
implies(not(A),not(truth)) = implies(truth,A),
inference(paramod,[status(thm)],[c_18,c_241]) ).
cnf(c_168,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_242]) ).
cnf(c_243,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_168,c_3]) ).
cnf(c_244,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_102,c_243]) ).
cnf(c_172,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_1,c_244]) ).
cnf(c_245,plain,
implies(implies(implies(not(truth),not(A)),not(A)),not(truth)) = A,
inference(paramod,[status(thm)],[c_168,c_46]) ).
cnf(c_246,plain,
implies(implies(truth,not(A)),not(truth)) = A,
inference(paramod,[status(thm)],[c_102,c_245]) ).
cnf(c_247,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_246]) ).
cnf(c_178,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_172,c_247]) ).
cnf(c_248,plain,
implies(implies(A,B),implies(not(B),implies(A,not(truth)))) = truth,
inference(paramod,[status(thm)],[c_172,c_2]) ).
cnf(c_186,plain,
implies(implies(A,B),implies(not(B),not(A))) = truth,
inference(paramod,[status(thm)],[c_172,c_248]) ).
cnf(c_249,plain,
implies(truth,implies(not(B),not(A))) = implies(A,B),
inference(paramod,[status(thm)],[c_186,c_24]) ).
cnf(c_191,plain,
implies(not(A),not(B)) = implies(B,A),
inference(paramod,[status(thm)],[c_1,c_249]) ).
cnf(c_250,plain,
implies(not(a),implies(not(not(implies(b,a))),not(b))) != truth,
inference(paramod,[status(thm)],[c_191,c_5]) ).
cnf(c_214,plain,
implies(not(a),implies(implies(b,a),not(b))) != truth,
inference(paramod,[status(thm)],[c_178,c_250]) ).
cnf(c_216,plain,
implies(not(A),implies(implies(B,A),not(B))) = truth,
inference(paramod,[status(thm)],[c_191,c_6]) ).
cnf(c_217,plain,
$false,
inference(resolve,[status(thm)],[c_216,c_214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL116-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 21:52:47 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 337142 was started by sandbox2 on n005,
% 0.16/0.42 % Fri Sep 25 21:52:47 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.20/0.51
% 0.20/0.51 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 0.20/0.51
% 0.20/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.51
% 0.20/0.51 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.20/0.51 % Length of proof is 32.
% 0.20/0.51 % Level of proof is 17.
% 0.20/0.51 % Maximum clause weight is 64.000.
% 0.20/0.51 % Given clauses 28.
% 0.20/0.51
% 0.20/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------