%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL138-1 : 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 : n016.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 07:58:05 AM UTC 2026
% Result : Unsatisfiable 22.25s 8.28s
% Output : CNFRefutation 22.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 5
% Syntax : Number of formulae : 95 ( 95 unt; 0 def)
% Number of atoms : 95 ( 94 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 163 ( 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_wajsberg_lemma,axiom,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
file('theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c_5,plain,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
inference(clausify,[status(thm)],[prove_wajsberg_lemma]) ).
cnf(c_6,plain,
implies(y,implies(x,z)) != implies(x,implies(y,z)),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_6245,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_6245]) ).
cnf(c_8,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_6246,plain,
implies(truth,implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))) = truth,
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_9,plain,
implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D)) = truth,
inference(paramod,[status(thm)],[c_1,c_6246]) ).
cnf(c_6247,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_13,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_6247]) ).
cnf(c_6248,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_6249,plain,
implies(implies(implies(A,B),B),A) = implies(implies(implies(B,A),A),A),
inference(paramod,[status(thm)],[c_3,c_6248]) ).
cnf(c_18,plain,
implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B),
inference(copy,[status(thm)],[c_6249]) ).
cnf(c_19,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_6250,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_6251,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_6250]) ).
cnf(c_25,plain,
implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B),
inference(copy,[status(thm)],[c_6251]) ).
cnf(c_6252,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_6253,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_6252]) ).
cnf(c_28,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_6253]) ).
cnf(c_36,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_28,c_13]) ).
cnf(c_42,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_36,c_7]) ).
cnf(c_6254,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_42,c_8]) ).
cnf(c_43,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_6254]) ).
cnf(c_6255,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_44,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_6255]) ).
cnf(c_6256,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_43,c_3]) ).
cnf(c_6257,plain,
implies(A,B) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_1,c_6256]) ).
cnf(c_46,plain,
implies(implies(implies(A,B),B),B) = implies(A,B),
inference(copy,[status(thm)],[c_6257]) ).
cnf(c_6258,plain,
implies(A,B) = implies(implies(implies(B,A),A),B),
inference(paramod,[status(thm)],[c_46,c_18]) ).
cnf(c_47,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(copy,[status(thm)],[c_6258]) ).
cnf(c_6259,plain,
implies(truth,implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))) = truth,
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_76,plain,
implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C)))) = truth,
inference(paramod,[status(thm)],[c_1,c_6259]) ).
cnf(c_6260,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_19,c_47]) ).
cnf(c_6261,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_1,c_6260]) ).
cnf(c_87,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_6261]) ).
cnf(c_6262,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_19,c_44]) ).
cnf(c_104,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_1,c_6262]) ).
cnf(c_6263,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_104,c_87]) ).
cnf(c_112,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_6263]) ).
cnf(c_6264,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_104,c_3]) ).
cnf(c_6265,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_6264]) ).
cnf(c_114,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_6265]) ).
cnf(c_6266,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_114,c_4]) ).
cnf(c_6267,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_112,c_6266]) ).
cnf(c_161,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_6267]) ).
cnf(c_6268,plain,
implies(truth,implies(A,implies(not(A),not(truth)))) = truth,
inference(paramod,[status(thm)],[c_161,c_4]) ).
cnf(c_187,plain,
implies(A,implies(not(A),not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_6268]) ).
cnf(c_6269,plain,
implies(truth,implies(not(A),not(truth))) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_187,c_3]) ).
cnf(c_6270,plain,
implies(not(A),not(truth)) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_1,c_6269]) ).
cnf(c_6271,plain,
implies(not(A),not(truth)) = implies(truth,A),
inference(paramod,[status(thm)],[c_19,c_6270]) ).
cnf(c_193,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_6271]) ).
cnf(c_6272,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_193,c_3]) ).
cnf(c_6273,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_104,c_6272]) ).
cnf(c_217,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_1,c_6273]) ).
cnf(c_6274,plain,
implies(implies(implies(not(truth),not(A)),not(A)),not(truth)) = A,
inference(paramod,[status(thm)],[c_193,c_47]) ).
cnf(c_6275,plain,
implies(implies(truth,not(A)),not(truth)) = A,
inference(paramod,[status(thm)],[c_104,c_6274]) ).
cnf(c_6276,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_6275]) ).
cnf(c_223,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_217,c_6276]) ).
cnf(c_6277,plain,
implies(implies(A,B),implies(not(B),implies(A,not(truth)))) = truth,
inference(paramod,[status(thm)],[c_217,c_2]) ).
cnf(c_232,plain,
implies(implies(A,B),implies(not(B),not(A))) = truth,
inference(paramod,[status(thm)],[c_217,c_6277]) ).
cnf(c_6278,plain,
implies(truth,implies(not(B),not(A))) = implies(A,B),
inference(paramod,[status(thm)],[c_232,c_25]) ).
cnf(c_238,plain,
implies(not(A),not(B)) = implies(B,A),
inference(paramod,[status(thm)],[c_1,c_6278]) ).
cnf(c_247,plain,
implies(not(A),not(implies(B,A))) = implies(implies(A,B),B),
inference(paramod,[status(thm)],[c_238,c_3]) ).
cnf(c_272,plain,
implies(implies(not(A),not(implies(B,A))),B) = implies(A,B),
inference(paramod,[status(thm)],[c_238,c_47]) ).
cnf(c_302,plain,
implies(A,not(B)) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_223,c_238]) ).
cnf(c_6279,plain,
implies(not(A),not(implies(B,A))) = implies(implies(B,A),A),
inference(paramod,[status(thm)],[c_247,c_3]) ).
cnf(c_446,plain,
implies(implies(A,B),B) = implies(not(B),not(implies(A,B))),
inference(copy,[status(thm)],[c_6279]) ).
cnf(c_6280,plain,
implies(not(implies(implies(A,B),B)),not(truth)) = implies(implies(implies(implies(A,B),B),A),A),
inference(paramod,[status(thm)],[c_7,c_247]) ).
cnf(c_6281,plain,
implies(not(implies(not(B),not(implies(A,B)))),not(truth)) = implies(implies(implies(implies(A,B),B),A),A),
inference(paramod,[status(thm)],[c_446,c_6280]) ).
cnf(c_6282,plain,
implies(truth,not(not(implies(not(B),not(implies(A,B)))))) = implies(implies(implies(implies(A,B),B),A),A),
inference(paramod,[status(thm)],[c_302,c_6281]) ).
cnf(c_6283,plain,
implies(truth,implies(not(B),not(implies(A,B)))) = implies(implies(implies(implies(A,B),B),A),A),
inference(paramod,[status(thm)],[c_223,c_6282]) ).
cnf(c_6284,plain,
implies(not(B),not(implies(A,B))) = implies(implies(implies(implies(A,B),B),A),A),
inference(paramod,[status(thm)],[c_1,c_6283]) ).
cnf(c_6285,plain,
implies(not(B),not(implies(A,B))) = implies(implies(implies(not(B),not(implies(A,B))),A),A),
inference(paramod,[status(thm)],[c_446,c_6284]) ).
cnf(c_6286,plain,
implies(not(B),not(implies(A,B))) = implies(implies(B,A),A),
inference(paramod,[status(thm)],[c_272,c_6285]) ).
cnf(c_450,plain,
implies(not(A),not(implies(B,A))) = implies(not(B),not(implies(A,B))),
inference(paramod,[status(thm)],[c_446,c_6286]) ).
cnf(c_6287,plain,
implies(implies(A,implies(B,C)),implies(B,implies(A,implies(truth,C)))) = truth,
inference(paramod,[status(thm)],[c_1,c_76]) ).
cnf(c_5218,plain,
implies(implies(A,implies(B,C)),implies(B,implies(A,C))) = truth,
inference(paramod,[status(thm)],[c_1,c_6287]) ).
cnf(c_6288,plain,
implies(not(implies(A,implies(B,C))),not(truth)) = implies(not(implies(B,implies(A,C))),not(implies(implies(A,implies(B,C)),implies(B,implies(A,C))))),
inference(paramod,[status(thm)],[c_5218,c_450]) ).
cnf(c_6289,plain,
implies(truth,not(not(implies(A,implies(B,C))))) = implies(not(implies(B,implies(A,C))),not(implies(implies(A,implies(B,C)),implies(B,implies(A,C))))),
inference(paramod,[status(thm)],[c_302,c_6288]) ).
cnf(c_6290,plain,
implies(truth,implies(A,implies(B,C))) = implies(not(implies(B,implies(A,C))),not(implies(implies(A,implies(B,C)),implies(B,implies(A,C))))),
inference(paramod,[status(thm)],[c_223,c_6289]) ).
cnf(c_6291,plain,
implies(A,implies(B,C)) = implies(not(implies(B,implies(A,C))),not(implies(implies(A,implies(B,C)),implies(B,implies(A,C))))),
inference(paramod,[status(thm)],[c_1,c_6290]) ).
cnf(c_6292,plain,
implies(A,implies(B,C)) = implies(not(implies(B,implies(A,C))),not(truth)),
inference(paramod,[status(thm)],[c_5218,c_6291]) ).
cnf(c_6293,plain,
implies(A,implies(B,C)) = implies(truth,not(not(implies(B,implies(A,C))))),
inference(paramod,[status(thm)],[c_302,c_6292]) ).
cnf(c_6294,plain,
implies(A,implies(B,C)) = implies(truth,implies(B,implies(A,C))),
inference(paramod,[status(thm)],[c_223,c_6293]) ).
cnf(c_6243,plain,
implies(A,implies(B,C)) = implies(B,implies(A,C)),
inference(paramod,[status(thm)],[c_1,c_6294]) ).
cnf(c_6244,plain,
$false,
inference(resolve,[status(thm)],[c_6243,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.43 % Computer : n016.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Fri Sep 25 21:59:06 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.44 % Process 3392093 was started by sandbox2 on n016,
% 0.15/5.44 % Fri Sep 25 21:59:06 2026
% 0.15/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.44
% 0.15/5.44 % From the command line: assign(max_seconds, 300).
% 22.25/8.28
% 22.25/8.28 % Assigning unary symbol not kb_weight 0 and highest precedence (7).
% 22.25/8.28
% 22.25/8.28 % SZS status Unsatisfiable for theBenchmark
% 22.25/8.28
% 22.25/8.28 % Proof 1 at 2.20 (+ 0.61) seconds.
% 22.25/8.28 % Length of proof is 40.
% 22.25/8.28 % Level of proof is 20.
% 22.25/8.28 % Maximum clause weight is 54.000.
% 22.25/8.28 % Given clauses 130.
% 22.25/8.28
% 22.25/8.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------