%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:57:59 AM UTC 2026
% Result : Unsatisfiable 31.36s 4.48s
% Output : CNFRefutation 31.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 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 : 154 ( 9 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wajsberg_1,axiom,
! [VAR_0] : implies(truth,VAR_0) = VAR_0,
file('theBenchmark.p',wajsberg_1) ).
cnf(c_2,plain,
implies(truth,A) = A,
inference(clausify,[status(thm)],[wajsberg_1]) ).
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_4,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(clausify,[status(thm)],[wajsberg_3]) ).
fof(lemma_3,axiom,
! [VAR_0] : implies(VAR_0,truth) = truth,
file('theBenchmark.p',lemma_3) ).
cnf(c_8,plain,
implies(A,truth) = truth,
inference(clausify,[status(thm)],[lemma_3]) ).
fof(lemma_4,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,implies(VAR_1,VAR_0)) = truth,
file('theBenchmark.p',lemma_4) ).
cnf(c_9,plain,
implies(A,implies(B,A)) = truth,
inference(clausify,[status(thm)],[lemma_4]) ).
fof(lemma_6,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(implies(VAR_0,VAR_1),implies(implies(VAR_2,VAR_0),implies(VAR_2,VAR_1))) = truth,
file('theBenchmark.p',lemma_6) ).
cnf(c_11,plain,
implies(implies(A,B),implies(implies(C,A),implies(C,B))) = truth,
inference(clausify,[status(thm)],[lemma_6]) ).
fof(lemma_7,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(VAR_0,implies(VAR_1,VAR_2)) = implies(VAR_1,implies(VAR_0,VAR_2)),
file('theBenchmark.p',lemma_7) ).
cnf(c_12,plain,
implies(A,implies(B,C)) = implies(B,implies(A,C)),
inference(clausify,[status(thm)],[lemma_7]) ).
fof(lemma_8,axiom,
! [VAR_0] : implies(VAR_0,not(truth)) = not(VAR_0),
file('theBenchmark.p',lemma_8) ).
cnf(c_13,plain,
implies(A,not(truth)) = not(A),
inference(clausify,[status(thm)],[lemma_8]) ).
fof(lemma_9,axiom,
! [VAR_0] : not(not(VAR_0)) = VAR_0,
file('theBenchmark.p',lemma_9) ).
cnf(c_14,plain,
not(not(A)) = A,
inference(clausify,[status(thm)],[lemma_9]) ).
fof(lemma_10,axiom,
! [VAR_0,VAR_1] : implies(not(VAR_0),not(VAR_1)) = implies(VAR_1,VAR_0),
file('theBenchmark.p',lemma_10) ).
cnf(c_15,plain,
implies(not(A),not(B)) = implies(B,A),
inference(clausify,[status(thm)],[lemma_10]) ).
fof(prove_wajsberg_mv_4,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c_16,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_mv_4]) ).
cnf(c_9385,plain,
implies(implies(b,implies(implies(a,b),a)),implies(b,a)) != truth,
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_17,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(paramod,[status(thm)],[c_12,c_9385]) ).
cnf(c_18,plain,
implies(implies(A,B),implies(C,implies(implies(C,A),B))) = truth,
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_9386,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_9387,plain,
implies(implies(implies(A,B),B),A) = implies(truth,implies(B,A)),
inference(paramod,[status(thm)],[c_9,c_9386]) ).
cnf(c_27,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(paramod,[status(thm)],[c_2,c_9387]) ).
cnf(c_9388,plain,
implies(implies(A,implies(B,C)),implies(A,C)) = implies(implies(implies(A,C),B),B),
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_9389,plain,
implies(A,implies(implies(A,implies(B,C)),C)) = implies(implies(implies(A,C),B),B),
inference(paramod,[status(thm)],[c_12,c_9388]) ).
cnf(c_57,plain,
implies(implies(implies(A,B),C),C) = implies(A,implies(implies(A,implies(C,B)),B)),
inference(copy,[status(thm)],[c_9389]) ).
cnf(c_9390,plain,
implies(A,not(B)) = implies(B,implies(A,not(truth))),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_75,plain,
implies(A,not(B)) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_13,c_9390]) ).
cnf(c_9391,plain,
implies(implies(A,B),not(A)) = implies(implies(not(A),not(B)),not(B)),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_9392,plain,
implies(A,not(implies(A,B))) = implies(implies(not(A),not(B)),not(B)),
inference(paramod,[status(thm)],[c_75,c_9391]) ).
cnf(c_9393,plain,
implies(A,not(implies(A,B))) = implies(B,not(implies(not(A),not(B)))),
inference(paramod,[status(thm)],[c_75,c_9392]) ).
cnf(c_85,plain,
implies(A,not(implies(not(B),not(A)))) = implies(B,not(implies(B,A))),
inference(copy,[status(thm)],[c_9393]) ).
cnf(c_86,plain,
implies(implies(not(A),not(B)),A) = implies(implies(A,B),B),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_9394,plain,
implies(not(A),not(implies(B,A))) = implies(implies(A,B),B),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_87,plain,
implies(implies(A,B),B) = implies(not(A),not(implies(B,A))),
inference(copy,[status(thm)],[c_9394]) ).
cnf(c_9395,plain,
implies(not(A),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_15,c_9]) ).
cnf(c_92,plain,
implies(A,implies(not(A),B)) = truth,
inference(paramod,[status(thm)],[c_12,c_9395]) ).
cnf(c_100,plain,
implies(A,implies(not(B),not(C))) = implies(C,implies(A,B)),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_102,plain,
implies(not(A),B) = implies(not(B),A),
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_104,plain,
implies(implies(not(A),not(B)),A) = implies(not(A),not(implies(B,A))),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_9396,plain,
implies(not(implies(A,B)),not(implies(C,implies(A,B)))) = implies(A,implies(implies(A,implies(C,B)),B)),
inference(paramod,[status(thm)],[c_87,c_57]) ).
cnf(c_107,plain,
implies(A,implies(implies(A,implies(B,C)),C)) = implies(not(implies(A,C)),not(implies(B,implies(A,C)))),
inference(copy,[status(thm)],[c_9396]) ).
cnf(c_9397,plain,
implies(implies(not(A),not(implies(B,A))),A) = implies(B,A),
inference(paramod,[status(thm)],[c_87,c_27]) ).
cnf(c_9398,plain,
implies(not(A),not(implies(implies(B,A),A))) = implies(B,A),
inference(paramod,[status(thm)],[c_104,c_9397]) ).
cnf(c_114,plain,
implies(not(A),not(implies(not(B),not(implies(A,B))))) = implies(B,A),
inference(paramod,[status(thm)],[c_87,c_9398]) ).
cnf(c_9399,plain,
implies(not(implies(b,a)),not(implies(implies(a,b),implies(b,a)))) != truth,
inference(paramod,[status(thm)],[c_107,c_17]) ).
cnf(c_119,plain,
implies(not(implies(b,a)),not(implies(b,implies(implies(a,b),a)))) != truth,
inference(paramod,[status(thm)],[c_12,c_9399]) ).
cnf(c_169,plain,
implies(not(implies(b,a)),not(implies(b,implies(not(a),not(implies(a,b)))))) != truth,
inference(paramod,[status(thm)],[c_15,c_119]) ).
cnf(c_9400,plain,
implies(implies(b,implies(not(a),not(implies(a,b)))),implies(b,a)) != truth,
inference(paramod,[status(thm)],[c_15,c_169]) ).
cnf(c_170,plain,
implies(b,implies(implies(b,implies(not(a),not(implies(a,b)))),a)) != truth,
inference(paramod,[status(thm)],[c_12,c_9400]) ).
cnf(c_9401,plain,
implies(A,truth) = implies(B,implies(A,implies(not(B),C))),
inference(paramod,[status(thm)],[c_92,c_12]) ).
cnf(c_9402,plain,
truth = implies(B,implies(A,implies(not(B),C))),
inference(paramod,[status(thm)],[c_8,c_9401]) ).
cnf(c_284,plain,
implies(A,implies(B,implies(not(A),C))) = truth,
inference(copy,[status(thm)],[c_9402]) ).
cnf(c_2182,plain,
implies(A,not(implies(A,B))) = implies(B,not(implies(B,A))),
inference(paramod,[status(thm)],[c_15,c_85]) ).
cnf(c_9403,plain,
implies(A,implies(not(B),not(not(C)))) = implies(not(implies(A,B)),C),
inference(paramod,[status(thm)],[c_100,c_102]) ).
cnf(c_9404,plain,
implies(A,implies(not(B),C)) = implies(not(implies(A,B)),C),
inference(paramod,[status(thm)],[c_14,c_9403]) ).
cnf(c_2950,plain,
implies(not(implies(A,B)),C) = implies(A,implies(not(B),C)),
inference(copy,[status(thm)],[c_9404]) ).
cnf(c_9405,plain,
implies(implies(A,implies(not(B),not(C))),implies(A,B)) = implies(not(C),not(implies(implies(A,B),C))),
inference(paramod,[status(thm)],[c_100,c_87]) ).
cnf(c_3136,plain,
implies(A,implies(implies(A,implies(not(B),not(C))),B)) = implies(not(C),not(implies(implies(A,B),C))),
inference(paramod,[status(thm)],[c_12,c_9405]) ).
cnf(c_9406,plain,
implies(not(implies(a,b)),not(implies(implies(b,a),implies(a,b)))) != truth,
inference(paramod,[status(thm)],[c_3136,c_170]) ).
cnf(c_9407,plain,
implies(not(implies(a,b)),not(implies(a,implies(implies(b,a),b)))) != truth,
inference(paramod,[status(thm)],[c_12,c_9406]) ).
cnf(c_3465,plain,
implies(a,implies(not(b),not(implies(a,implies(implies(b,a),b))))) != truth,
inference(paramod,[status(thm)],[c_2950,c_9407]) ).
cnf(c_3500,plain,
implies(a,implies(not(b),not(implies(a,implies(not(b),not(implies(b,a))))))) != truth,
inference(paramod,[status(thm)],[c_15,c_3465]) ).
cnf(c_9408,plain,
implies(not(A),not(implies(not(implies(B,implies(not(A),C))),not(truth)))) = implies(implies(B,implies(not(A),C)),A),
inference(paramod,[status(thm)],[c_284,c_114]) ).
cnf(c_9409,plain,
implies(not(A),not(implies(truth,not(not(implies(B,implies(not(A),C))))))) = implies(implies(B,implies(not(A),C)),A),
inference(paramod,[status(thm)],[c_75,c_9408]) ).
cnf(c_9410,plain,
implies(not(A),not(implies(truth,implies(B,implies(not(A),C))))) = implies(implies(B,implies(not(A),C)),A),
inference(paramod,[status(thm)],[c_14,c_9409]) ).
cnf(c_9411,plain,
implies(not(A),not(implies(B,implies(not(A),C)))) = implies(implies(B,implies(not(A),C)),A),
inference(paramod,[status(thm)],[c_2,c_9410]) ).
cnf(c_5753,plain,
implies(implies(A,implies(not(B),C)),B) = implies(not(B),not(implies(A,implies(not(B),C)))),
inference(copy,[status(thm)],[c_9411]) ).
cnf(c_9412,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = implies(not(B),not(implies(not(implies(B,A)),B))),
inference(paramod,[status(thm)],[c_2182,c_87]) ).
cnf(c_9413,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = implies(not(B),not(implies(not(B),implies(B,A)))),
inference(paramod,[status(thm)],[c_102,c_9412]) ).
cnf(c_9414,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = implies(not(B),not(implies(B,implies(not(B),A)))),
inference(paramod,[status(thm)],[c_12,c_9413]) ).
cnf(c_9415,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = implies(not(B),not(truth)),
inference(paramod,[status(thm)],[c_92,c_9414]) ).
cnf(c_9416,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = implies(truth,not(not(B))),
inference(paramod,[status(thm)],[c_75,c_9415]) ).
cnf(c_9417,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = implies(truth,B),
inference(paramod,[status(thm)],[c_14,c_9416]) ).
cnf(c_6634,plain,
implies(implies(A,not(implies(A,B))),not(implies(B,A))) = B,
inference(paramod,[status(thm)],[c_2,c_9417]) ).
cnf(c_9418,plain,
implies(implies(not(implies(A,B)),not(implies(B,A))),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_6634,c_18]) ).
cnf(c_9419,plain,
implies(implies(A,implies(not(B),not(implies(B,A)))),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_2950,c_9418]) ).
cnf(c_9420,plain,
implies(A,implies(implies(A,implies(not(B),not(implies(B,A)))),B)) = truth,
inference(paramod,[status(thm)],[c_12,c_9419]) ).
cnf(c_9383,plain,
implies(A,implies(not(B),not(implies(A,implies(not(B),not(implies(B,A))))))) = truth,
inference(paramod,[status(thm)],[c_5753,c_9420]) ).
cnf(c_9384,plain,
$false,
inference(resolve,[status(thm)],[c_9383,c_3500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 21:54:57 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2353594 was started by sandbox2 on n015,
% 0.18/0.45 % Fri Sep 25 21:54:57 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 31.36/4.48
% 31.36/4.48 % SZS status Unsatisfiable for theBenchmark
% 31.36/4.48
% 31.36/4.48 % Proof 1 at 3.17 (+ 0.80) seconds.
% 31.36/4.48 % Length of proof is 37.
% 31.36/4.48 % Level of proof is 8.
% 31.36/4.48 % Maximum clause weight is 21.000.
% 31.36/4.48 % Given clauses 230.
% 31.36/4.48
% 31.36/4.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------