%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT091-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:49:40 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.59s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 97 ( 97 unt; 0 def)
% Number of atoms : 97 ( 96 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 195 ( 34 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wal_absorbtion_1,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_1),meet(VAR_0,join(VAR_0,VAR_1))) = VAR_0,
file('theBenchmark.p',wal_absorbtion_1) ).
cnf(c_1,plain,
join(meet(A,B),meet(A,join(A,B))) = A,
inference(clausify,[status(thm)],[wal_absorbtion_1]) ).
fof(wal_absorbtion_2,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_0),meet(VAR_1,join(VAR_0,VAR_0))) = VAR_0,
file('theBenchmark.p',wal_absorbtion_2) ).
cnf(c_2,plain,
join(meet(A,A),meet(B,join(A,A))) = A,
inference(clausify,[status(thm)],[wal_absorbtion_2]) ).
fof(wal_absorbtion_3,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_1),meet(VAR_1,join(VAR_0,VAR_1))) = VAR_1,
file('theBenchmark.p',wal_absorbtion_3) ).
cnf(c_3,plain,
join(meet(A,B),meet(B,join(A,B))) = B,
inference(clausify,[status(thm)],[wal_absorbtion_3]) ).
fof(wal_absorbtion_4,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_2,VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',wal_absorbtion_4) ).
cnf(c_4,plain,
meet(meet(join(A,B),join(C,A)),A) = A,
inference(clausify,[status(thm)],[wal_absorbtion_4]) ).
fof(wal_absorbtion_5,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_2,VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',wal_absorbtion_5) ).
cnf(c_5,plain,
join(join(meet(A,B),meet(C,A)),A) = A,
inference(clausify,[status(thm)],[wal_absorbtion_5]) ).
fof(prove_normal_axioms_4,axiom,
join(b,a) != join(a,b),
file('theBenchmark.p',prove_normal_axioms_4) ).
cnf(c_6,plain,
join(b,a) != join(a,b),
inference(clausify,[status(thm)],[prove_normal_axioms_4]) ).
cnf(c_7,plain,
join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
join(meet(meet(A,A),meet(B,join(A,A))),meet(meet(A,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_16,plain,
join(meet(A,A),join(A,A)) = A,
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_19,plain,
meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_24,plain,
meet(meet(join(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_25,plain,
join(join(A,meet(B,meet(join(A,C),join(D,A)))),meet(join(A,C),join(D,A))) = meet(join(A,C),join(D,A)),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_26,plain,
join(join(meet(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_306,plain,
join(meet(A,meet(meet(join(A,B),join(C,A)),join(meet(join(A,B),join(C,A)),A))),meet(meet(meet(join(A,B),join(C,A)),A),meet(join(A,B),join(C,A)))) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_307,plain,
join(meet(A,meet(meet(join(A,B),join(C,A)),join(meet(join(A,B),join(C,A)),A))),meet(A,meet(join(A,B),join(C,A)))) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_306]) ).
cnf(c_32,plain,
join(meet(A,meet(meet(join(A,B),join(C,A)),join(meet(join(A,B),join(C,A)),A))),meet(A,meet(join(A,B),join(C,A)))) = A,
inference(paramod,[status(thm)],[c_4,c_307]) ).
cnf(c_34,plain,
join(meet(meet(A,A),join(A,A)),meet(meet(A,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_35,plain,
join(meet(meet(A,A),join(A,A)),meet(join(A,A),A)) = join(A,A),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_39,plain,
meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_45,plain,
join(meet(join(meet(A,B),A),A),meet(join(meet(A,B),A),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_51,plain,
join(join(A,meet(join(A,B),A)),meet(join(A,B),A)) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_24,c_26]) ).
cnf(c_308,plain,
meet(meet(meet(join(A,B),join(C,A)),A),meet(meet(join(A,B),join(C,A)),A)) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_39]) ).
cnf(c_309,plain,
meet(A,meet(meet(join(A,B),join(C,A)),A)) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_308]) ).
cnf(c_310,plain,
meet(A,A) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_309]) ).
cnf(c_62,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_4,c_310]) ).
cnf(c_65,plain,
join(join(meet(A,B),meet(A,meet(A,B))),meet(A,meet(A,B))) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_39,c_26]) ).
cnf(c_76,plain,
join(meet(A,join(A,A)),meet(join(A,A),A)) = join(A,A),
inference(paramod,[status(thm)],[c_62,c_35]) ).
cnf(c_311,plain,
join(meet(A,join(A,A)),meet(meet(A,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_34]) ).
cnf(c_312,plain,
join(meet(A,join(A,A)),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_311]) ).
cnf(c_313,plain,
join(meet(A,join(A,A)),A) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_312]) ).
cnf(c_77,plain,
join(meet(A,join(A,A)),A) = A,
inference(paramod,[status(thm)],[c_62,c_313]) ).
cnf(c_314,plain,
join(meet(A,meet(B,join(A,A))),meet(meet(A,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_8]) ).
cnf(c_315,plain,
join(meet(A,meet(B,join(A,A))),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_314]) ).
cnf(c_316,plain,
join(meet(A,meet(B,join(A,A))),A) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_315]) ).
cnf(c_83,plain,
join(meet(A,meet(B,join(A,A))),A) = A,
inference(paramod,[status(thm)],[c_62,c_316]) ).
cnf(c_84,plain,
join(A,meet(B,join(A,A))) = A,
inference(paramod,[status(thm)],[c_62,c_2]) ).
cnf(c_95,plain,
meet(join(A,A),A) = A,
inference(paramod,[status(thm)],[c_62,c_4]) ).
cnf(c_317,plain,
join(meet(A,join(A,A)),A) = join(A,A),
inference(paramod,[status(thm)],[c_95,c_76]) ).
cnf(c_318,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_77,c_317]) ).
cnf(c_98,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_318]) ).
cnf(c_100,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_98,c_84]) ).
cnf(c_101,plain,
join(meet(A,meet(B,A)),A) = A,
inference(paramod,[status(thm)],[c_98,c_83]) ).
cnf(c_105,plain,
meet(join(meet(A,B),A),A) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_98,c_45]) ).
cnf(c_319,plain,
join(meet(A,B),meet(A,meet(A,B))) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_100,c_65]) ).
cnf(c_320,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_100,c_319]) ).
cnf(c_110,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_320]) ).
cnf(c_321,plain,
join(A,meet(join(A,B),A)) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_100,c_51]) ).
cnf(c_322,plain,
A = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_100,c_321]) ).
cnf(c_111,plain,
meet(join(A,B),A) = A,
inference(copy,[status(thm)],[c_322]) ).
cnf(c_115,plain,
meet(meet(A,join(B,A)),A) = A,
inference(paramod,[status(thm)],[c_98,c_4]) ).
cnf(c_119,plain,
join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_111,c_1]) ).
cnf(c_121,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_3,c_111]) ).
cnf(c_323,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(meet(join(A,B),A),join(A,B))) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_111,c_7]) ).
cnf(c_324,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_111,c_323]) ).
cnf(c_124,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A,
inference(paramod,[status(thm)],[c_111,c_324]) ).
cnf(c_126,plain,
meet(A,join(meet(A,B),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_26,c_111]) ).
cnf(c_129,plain,
join(meet(A,B),B) = B,
inference(paramod,[status(thm)],[c_121,c_101]) ).
cnf(c_325,plain,
join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,meet(A,B)),A)) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_110,c_7]) ).
cnf(c_326,plain,
join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_110,c_325]) ).
cnf(c_136,plain,
join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_110,c_326]) ).
cnf(c_141,plain,
join(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_115,c_1]) ).
cnf(c_327,plain,
meet(meet(join(A,B),join(C,A)),join(A,meet(join(A,B),join(C,A)))) = join(meet(meet(join(A,B),join(C,A)),A),meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_4,c_126]) ).
cnf(c_161,plain,
meet(meet(join(A,B),join(C,A)),join(A,meet(join(A,B),join(C,A)))) = join(A,meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_4,c_327]) ).
cnf(c_328,plain,
meet(join(meet(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_126,c_115]) ).
cnf(c_164,plain,
join(meet(A,B),A) = A,
inference(paramod,[status(thm)],[c_105,c_328]) ).
cnf(c_329,plain,
join(A,meet(meet(A,join(B,A)),A)) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_164,c_141]) ).
cnf(c_330,plain,
join(A,A) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_115,c_329]) ).
cnf(c_331,plain,
A = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_98,c_330]) ).
cnf(c_167,plain,
meet(A,join(B,A)) = A,
inference(copy,[status(thm)],[c_331]) ).
cnf(c_332,plain,
meet(join(A,B),join(C,A)) = join(A,meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_167,c_161]) ).
cnf(c_169,plain,
join(A,meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)),
inference(copy,[status(thm)],[c_332]) ).
cnf(c_170,plain,
meet(join(A,B),join(join(A,B),A)) = join(A,B),
inference(paramod,[status(thm)],[c_169,c_119]) ).
cnf(c_333,plain,
join(meet(A,join(A,B)),meet(A,join(A,B))) = A,
inference(paramod,[status(thm)],[c_170,c_124]) ).
cnf(c_171,plain,
meet(A,join(A,B)) = A,
inference(paramod,[status(thm)],[c_98,c_333]) ).
cnf(c_334,plain,
join(meet(meet(A,B),A),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_171,c_136]) ).
cnf(c_172,plain,
meet(meet(A,B),A) = meet(A,B),
inference(paramod,[status(thm)],[c_98,c_334]) ).
cnf(c_335,plain,
join(meet(A,meet(join(A,B),join(C,A))),meet(A,meet(join(A,B),join(C,A)))) = A,
inference(paramod,[status(thm)],[c_171,c_32]) ).
cnf(c_173,plain,
meet(A,meet(join(A,B),join(C,A))) = A,
inference(paramod,[status(thm)],[c_98,c_335]) ).
cnf(c_187,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_172,c_100]) ).
cnf(c_196,plain,
meet(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_187,c_19]) ).
cnf(c_336,plain,
meet(meet(A,B),meet(B,A)) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_196,c_172]) ).
cnf(c_337,plain,
meet(B,A) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_196,c_336]) ).
cnf(c_205,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_196,c_337]) ).
cnf(c_233,plain,
meet(A,meet(join(B,A),join(A,C))) = A,
inference(paramod,[status(thm)],[c_205,c_173]) ).
cnf(c_338,plain,
join(join(A,B),meet(join(A,B),join(B,A))) = meet(join(A,B),join(B,A)),
inference(paramod,[status(thm)],[c_233,c_25]) ).
cnf(c_339,plain,
join(A,B) = meet(join(A,B),join(B,A)),
inference(paramod,[status(thm)],[c_187,c_338]) ).
cnf(c_295,plain,
meet(join(A,B),join(B,A)) = join(A,B),
inference(copy,[status(thm)],[c_339]) ).
cnf(c_303,plain,
join(join(A,B),join(B,A)) = join(A,B),
inference(paramod,[status(thm)],[c_295,c_100]) ).
cnf(c_340,plain,
join(join(A,B),join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_295,c_129]) ).
cnf(c_304,plain,
join(A,B) = join(B,A),
inference(paramod,[status(thm)],[c_303,c_340]) ).
cnf(c_305,plain,
$false,
inference(resolve,[status(thm)],[c_304,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT091-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.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 20:05:22 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 960584 was started by sandbox2 on n003,
% 0.18/0.45 % Fri Sep 25 20:05:22 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).
% 0.23/0.59
% 0.23/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.59
% 0.23/0.59 % Proof 1 at 0.09 (+ 0.04) seconds.
% 0.23/0.59 % Length of proof is 56.
% 0.23/0.59 % Level of proof is 22.
% 0.23/0.59 % Maximum clause weight is 72.000.
% 0.23/0.59 % Given clauses 54.
% 0.23/0.59
% 0.23/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------