%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL109-2 : 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 : n019.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 07:58:00 AM UTC 2026
% Result : Unsatisfiable 98.67s 14.04s
% Output : CNFRefutation 98.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 5
% Syntax : Number of formulae : 113 ( 113 unt; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 17 ( 17 ~; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 155 ( 13 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_mv_4,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c_5,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_mv_4]) ).
cnf(c_9874,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_9874]) ).
cnf(c_7,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_9875,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_8,plain,
implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D)) = truth,
inference(paramod,[status(thm)],[c_1,c_9875]) ).
cnf(c_9876,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_9876]) ).
cnf(c_17,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_19,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_9877,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_9878,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_9877]) ).
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_9878]) ).
cnf(c_9879,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_9880,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_9879]) ).
cnf(c_28,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_9880]) ).
cnf(c_9881,plain,
implies(truth,implies(implies(implies(implies(A,B),B),C),implies(A,C))) = truth,
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_29,plain,
implies(implies(implies(implies(A,B),B),C),implies(A,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_9881]) ).
cnf(c_36,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_28,c_12]) ).
cnf(c_42,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_9882,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_42,c_7]) ).
cnf(c_43,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_9882]) ).
cnf(c_9883,plain,
implies(implies(implies(A,B),B),A) = implies(truth,implies(B,A)),
inference(paramod,[status(thm)],[c_43,c_17]) ).
cnf(c_44,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(paramod,[status(thm)],[c_1,c_9883]) ).
cnf(c_9884,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_45,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_9884]) ).
cnf(c_9885,plain,
implies(truth,A) = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_9886,plain,
A = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_1,c_9885]) ).
cnf(c_49,plain,
implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))) = A,
inference(copy,[status(thm)],[c_9886]) ).
cnf(c_9887,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_19,c_44]) ).
cnf(c_9888,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_1,c_9887]) ).
cnf(c_56,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_9888]) ).
cnf(c_9889,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(not(not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_56,c_44]) ).
cnf(c_9890,plain,
implies(truth,not(truth)) = implies(not(not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_28,c_9889]) ).
cnf(c_9891,plain,
not(truth) = implies(not(not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_9890]) ).
cnf(c_80,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(copy,[status(thm)],[c_9891]) ).
cnf(c_9892,plain,
implies(truth,implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C))) = truth,
inference(paramod,[status(thm)],[c_45,c_2]) ).
cnf(c_88,plain,
implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C)) = truth,
inference(paramod,[status(thm)],[c_1,c_9892]) ).
cnf(c_9893,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_19,c_45]) ).
cnf(c_96,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_1,c_9893]) ).
cnf(c_9894,plain,
implies(implies(implies(A,not(not(truth))),not(truth)),not(truth)) = truth,
inference(paramod,[status(thm)],[c_80,c_45]) ).
cnf(c_9895,plain,
implies(implies(not(truth),implies(A,not(not(truth)))),implies(A,not(not(truth)))) = truth,
inference(paramod,[status(thm)],[c_3,c_9894]) ).
cnf(c_9896,plain,
implies(truth,implies(A,not(not(truth)))) = truth,
inference(paramod,[status(thm)],[c_96,c_9895]) ).
cnf(c_100,plain,
implies(A,not(not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_9896]) ).
cnf(c_9897,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_100,c_56]) ).
cnf(c_101,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_9897]) ).
cnf(c_9898,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_96,c_3]) ).
cnf(c_9899,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_9898]) ).
cnf(c_103,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_9899]) ).
cnf(c_9900,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_103,c_4]) ).
cnf(c_9901,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_101,c_9900]) ).
cnf(c_138,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_9901]) ).
cnf(c_9902,plain,
implies(truth,implies(A,implies(not(A),not(truth)))) = truth,
inference(paramod,[status(thm)],[c_138,c_4]) ).
cnf(c_150,plain,
implies(A,implies(not(A),not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_9902]) ).
cnf(c_9903,plain,
implies(truth,implies(not(A),not(truth))) = A,
inference(paramod,[status(thm)],[c_150,c_49]) ).
cnf(c_154,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_9903]) ).
cnf(c_9904,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_154,c_3]) ).
cnf(c_9905,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_96,c_9904]) ).
cnf(c_9906,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_1,c_9905]) ).
cnf(c_158,plain,
not(A) = implies(A,not(truth)),
inference(copy,[status(thm)],[c_9906]) ).
cnf(c_9907,plain,
not(implies(A,not(truth))) = implies(implies(not(truth),A),A),
inference(paramod,[status(thm)],[c_158,c_3]) ).
cnf(c_9908,plain,
not(implies(A,not(truth))) = implies(truth,A),
inference(paramod,[status(thm)],[c_96,c_9907]) ).
cnf(c_170,plain,
not(implies(A,not(truth))) = A,
inference(paramod,[status(thm)],[c_1,c_9908]) ).
cnf(c_181,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_158,c_154]) ).
cnf(c_182,plain,
implies(implies(A,not(B)),implies(B,not(A))) = truth,
inference(paramod,[status(thm)],[c_181,c_4]) ).
cnf(c_9909,plain,
implies(truth,implies(A,not(B))) = implies(implies(implies(A,not(B)),implies(B,not(A))),implies(B,not(A))),
inference(paramod,[status(thm)],[c_182,c_3]) ).
cnf(c_9910,plain,
implies(A,not(B)) = implies(implies(implies(A,not(B)),implies(B,not(A))),implies(B,not(A))),
inference(paramod,[status(thm)],[c_1,c_9909]) ).
cnf(c_9911,plain,
implies(A,not(B)) = implies(truth,implies(B,not(A))),
inference(paramod,[status(thm)],[c_182,c_9910]) ).
cnf(c_376,plain,
implies(A,not(B)) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_1,c_9911]) ).
cnf(c_380,plain,
implies(implies(A,B),implies(not(B),not(A))) = truth,
inference(paramod,[status(thm)],[c_181,c_182]) ).
cnf(c_9912,plain,
implies(truth,implies(not(B),not(A))) = implies(A,B),
inference(paramod,[status(thm)],[c_380,c_25]) ).
cnf(c_396,plain,
implies(not(A),not(B)) = implies(B,A),
inference(paramod,[status(thm)],[c_1,c_9912]) ).
cnf(c_9913,plain,
implies(A,implies(B,not(truth))) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_158,c_376]) ).
cnf(c_412,plain,
implies(A,not(B)) = implies(B,implies(A,not(truth))),
inference(copy,[status(thm)],[c_9913]) ).
cnf(c_9914,plain,
implies(A,B) = implies(implies(B,not(truth)),not(A)),
inference(paramod,[status(thm)],[c_170,c_376]) ).
cnf(c_413,plain,
implies(implies(A,not(truth)),not(B)) = implies(B,A),
inference(copy,[status(thm)],[c_9914]) ).
cnf(c_442,plain,
implies(implies(implies(a,b),implies(b,a)),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_396,c_5]) ).
cnf(c_470,plain,
implies(not(A),implies(B,not(truth))) = implies(B,A),
inference(paramod,[status(thm)],[c_158,c_396]) ).
cnf(c_9915,plain,
implies(A,B) = implies(implies(B,not(truth)),implies(A,not(truth))),
inference(paramod,[status(thm)],[c_170,c_412]) ).
cnf(c_592,plain,
implies(implies(A,not(truth)),implies(B,not(truth))) = implies(B,A),
inference(copy,[status(thm)],[c_9915]) ).
cnf(c_9916,plain,
implies(implies(A,B),implies(A,not(truth))) = implies(implies(implies(A,not(truth)),not(B)),not(B)),
inference(paramod,[status(thm)],[c_470,c_3]) ).
cnf(c_802,plain,
implies(implies(implies(A,not(truth)),not(B)),not(B)) = implies(implies(A,B),implies(A,not(truth))),
inference(copy,[status(thm)],[c_9916]) ).
cnf(c_876,plain,
implies(implies(implies(a,b),implies(not(a),implies(b,not(truth)))),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_470,c_442]) ).
cnf(c_9917,plain,
implies(truth,implies(implies(A,implies(B,C)),implies(B,implies(A,C)))) = truth,
inference(paramod,[status(thm)],[c_29,c_8]) ).
cnf(c_1546,plain,
implies(implies(A,implies(B,C)),implies(B,implies(A,C))) = truth,
inference(paramod,[status(thm)],[c_1,c_9917]) ).
cnf(c_4142,plain,
implies(implies(implies(implies(not(a),implies(b,not(truth))),not(truth)),implies(implies(a,b),not(truth))),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_592,c_876]) ).
cnf(c_9918,plain,
implies(truth,implies(A,implies(B,C))) = implies(implies(implies(A,implies(B,C)),implies(B,implies(A,C))),implies(B,implies(A,C))),
inference(paramod,[status(thm)],[c_1546,c_3]) ).
cnf(c_9919,plain,
implies(A,implies(B,C)) = implies(implies(implies(A,implies(B,C)),implies(B,implies(A,C))),implies(B,implies(A,C))),
inference(paramod,[status(thm)],[c_1,c_9918]) ).
cnf(c_9920,plain,
implies(A,implies(B,C)) = implies(truth,implies(B,implies(A,C))),
inference(paramod,[status(thm)],[c_1546,c_9919]) ).
cnf(c_8099,plain,
implies(A,implies(B,C)) = implies(B,implies(A,C)),
inference(paramod,[status(thm)],[c_1,c_9920]) ).
cnf(c_9921,plain,
implies(implies(implies(implies(b,implies(not(a),not(truth))),not(truth)),implies(implies(a,b),not(truth))),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_8099,c_4142]) ).
cnf(c_9922,plain,
implies(implies(implies(implies(b,a),not(truth)),implies(implies(a,b),not(truth))),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_154,c_9921]) ).
cnf(c_9923,plain,
implies(implies(implies(a,b),implies(implies(implies(b,a),not(truth)),not(truth))),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_8099,c_9922]) ).
cnf(c_9924,plain,
implies(implies(implies(a,b),implies(b,a)),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_103,c_9923]) ).
cnf(c_9147,plain,
implies(implies(b,implies(implies(a,b),a)),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_8099,c_9924]) ).
cnf(c_9717,plain,
implies(implies(implies(A,not(truth)),not(B)),not(B)) = implies(A,implies(implies(A,B),not(truth))),
inference(paramod,[status(thm)],[c_8099,c_802]) ).
cnf(c_9925,plain,
implies(implies(implies(implies(implies(a,b),a),not(truth)),not(b)),implies(not(a),not(b))) != truth,
inference(paramod,[status(thm)],[c_413,c_9147]) ).
cnf(c_9926,plain,
implies(not(a),implies(implies(implies(implies(implies(a,b),a),not(truth)),not(b)),not(b))) != truth,
inference(paramod,[status(thm)],[c_8099,c_9925]) ).
cnf(c_9927,plain,
implies(not(a),implies(implies(implies(a,b),a),implies(implies(implies(implies(a,b),a),b),not(truth)))) != truth,
inference(paramod,[status(thm)],[c_9717,c_9926]) ).
cnf(c_9928,plain,
implies(implies(implies(a,b),a),implies(not(a),implies(implies(implies(implies(a,b),a),b),not(truth)))) != truth,
inference(paramod,[status(thm)],[c_8099,c_9927]) ).
cnf(c_9929,plain,
implies(implies(implies(a,b),a),implies(implies(implies(implies(a,b),a),b),implies(not(a),not(truth)))) != truth,
inference(paramod,[status(thm)],[c_8099,c_9928]) ).
cnf(c_9930,plain,
implies(implies(implies(a,b),a),implies(implies(implies(implies(a,b),a),b),a)) != truth,
inference(paramod,[status(thm)],[c_154,c_9929]) ).
cnf(c_9931,plain,
truth != truth,
inference(paramod,[status(thm)],[c_88,c_9930]) ).
cnf(c_9873,plain,
$false,
inference(copy,[status(thm)],[c_9931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:51:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3814997 was started by sandbox2 on n019,
% 0.08/0.36 % Fri Sep 25 21:51:48 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 98.67/14.04
% 98.67/14.04 % SZS status Unsatisfiable for theBenchmark
% 98.67/14.04
% 98.67/14.04 % Proof 1 at 4.39 (+ 0.81) seconds.
% 98.67/14.04 % Length of proof is 50.
% 98.67/14.04 % Level of proof is 23.
% 98.67/14.04 % Maximum clause weight is 95.000.
% 98.67/14.04 % Given clauses 270.
% 98.67/14.04
% 98.67/14.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
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