%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT029-1 : TPTP v9.3.1. Released v2.2.0.
% 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 07:49:34 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 6
% Syntax : Number of formulae : 111 ( 104 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 23 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 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 : 222 ( 39 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,axiom,
( join(b,a) != join(a,b)
| join(a,a) != a
| meet(b,a) != meet(a,b)
| meet(a,a) != a ),
file('theBenchmark.p',prove_normal_axioms) ).
cnf(c_6,plain,
( join(b,a) != join(a,b)
| join(a,a) != a
| meet(b,a) != meet(a,b)
| meet(a,a) != a ),
inference(clausify,[status(thm)],[prove_normal_axioms]) ).
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_13,plain,
join(A,meet(meet(join(A,B),join(C,A)),join(meet(join(A,B),join(C,A)),A))) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_4,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_321,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_322,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_321]) ).
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_322]) ).
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_323,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_324,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_323]) ).
cnf(c_325,plain,
meet(A,A) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_324]) ).
cnf(c_62,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_4,c_325]) ).
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_326,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_327,plain,
join(meet(A,join(A,A)),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_326]) ).
cnf(c_328,plain,
join(meet(A,join(A,A)),A) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_327]) ).
cnf(c_77,plain,
join(meet(A,join(A,A)),A) = A,
inference(paramod,[status(thm)],[c_62,c_328]) ).
cnf(c_329,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_330,plain,
join(meet(A,meet(B,join(A,A))),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_329]) ).
cnf(c_331,plain,
join(meet(A,meet(B,join(A,A))),A) = meet(A,A),
inference(paramod,[status(thm)],[c_62,c_330]) ).
cnf(c_83,plain,
join(meet(A,meet(B,join(A,A))),A) = A,
inference(paramod,[status(thm)],[c_62,c_331]) ).
cnf(c_332,plain,
( join(b,a) != join(a,b)
| join(a,a) != a
| meet(b,a) != meet(a,b)
| a != a ),
inference(paramod,[status(thm)],[c_62,c_6]) ).
cnf(c_84,plain,
( join(b,a) != join(a,b)
| join(a,a) != a
| meet(b,a) != meet(a,b) ),
inference(copy,[status(thm)],[c_332]) ).
cnf(c_85,plain,
join(A,meet(B,join(A,A))) = A,
inference(paramod,[status(thm)],[c_62,c_2]) ).
cnf(c_96,plain,
meet(join(A,A),A) = A,
inference(paramod,[status(thm)],[c_62,c_4]) ).
cnf(c_333,plain,
join(meet(A,join(A,A)),A) = join(A,A),
inference(paramod,[status(thm)],[c_96,c_76]) ).
cnf(c_334,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_77,c_333]) ).
cnf(c_99,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_334]) ).
cnf(c_101,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_99,c_85]) ).
cnf(c_335,plain,
( join(b,a) != join(a,b)
| a != a
| meet(b,a) != meet(a,b) ),
inference(paramod,[status(thm)],[c_99,c_84]) ).
cnf(c_102,plain,
( join(b,a) != join(a,b)
| meet(b,a) != meet(a,b) ),
inference(copy,[status(thm)],[c_335]) ).
cnf(c_103,plain,
join(meet(A,meet(B,A)),A) = A,
inference(paramod,[status(thm)],[c_99,c_83]) ).
cnf(c_107,plain,
meet(join(meet(A,B),A),A) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_99,c_45]) ).
cnf(c_336,plain,
join(meet(A,B),meet(A,meet(A,B))) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_101,c_65]) ).
cnf(c_337,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_101,c_336]) ).
cnf(c_112,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_337]) ).
cnf(c_338,plain,
join(A,meet(join(A,B),A)) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_101,c_51]) ).
cnf(c_339,plain,
A = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_101,c_338]) ).
cnf(c_113,plain,
meet(join(A,B),A) = A,
inference(copy,[status(thm)],[c_339]) ).
cnf(c_117,plain,
meet(meet(A,join(B,A)),A) = A,
inference(paramod,[status(thm)],[c_99,c_4]) ).
cnf(c_121,plain,
join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_113,c_1]) ).
cnf(c_123,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_3,c_113]) ).
cnf(c_340,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_113,c_7]) ).
cnf(c_341,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_113,c_340]) ).
cnf(c_126,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A,
inference(paramod,[status(thm)],[c_113,c_341]) ).
cnf(c_128,plain,
meet(A,join(meet(A,B),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_26,c_113]) ).
cnf(c_131,plain,
join(meet(A,B),B) = B,
inference(paramod,[status(thm)],[c_123,c_103]) ).
cnf(c_342,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_112,c_7]) ).
cnf(c_343,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_112,c_342]) ).
cnf(c_140,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_112,c_343]) ).
cnf(c_344,plain,
join(join(meet(A,B),A),meet(meet(A,join(C,join(meet(A,B),A))),join(meet(join(join(meet(A,B),A),A),join(C,join(meet(A,B),A))),join(meet(A,B),A)))) = meet(join(join(meet(A,B),A),A),join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_26,c_13]) ).
cnf(c_345,plain,
join(join(meet(A,B),A),meet(meet(A,join(C,join(meet(A,B),A))),join(meet(A,join(C,join(meet(A,B),A))),join(meet(A,B),A)))) = meet(join(join(meet(A,B),A),A),join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_26,c_344]) ).
cnf(c_167,plain,
join(join(meet(A,B),A),meet(meet(A,join(C,join(meet(A,B),A))),join(meet(A,join(C,join(meet(A,B),A))),join(meet(A,B),A)))) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_26,c_345]) ).
cnf(c_346,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_128]) ).
cnf(c_172,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_346]) ).
cnf(c_347,plain,
meet(join(meet(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_128,c_117]) ).
cnf(c_175,plain,
join(meet(A,B),A) = A,
inference(paramod,[status(thm)],[c_107,c_347]) ).
cnf(c_348,plain,
join(A,meet(meet(A,join(C,join(meet(A,B),A))),join(meet(A,join(C,join(meet(A,B),A))),join(meet(A,B),A)))) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_175,c_167]) ).
cnf(c_349,plain,
join(A,meet(meet(A,join(C,A)),join(meet(A,join(C,join(meet(A,B),A))),join(meet(A,B),A)))) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_175,c_348]) ).
cnf(c_350,plain,
join(A,meet(meet(A,join(C,A)),join(meet(A,join(C,A)),join(meet(A,B),A)))) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_175,c_349]) ).
cnf(c_351,plain,
join(A,meet(meet(A,join(C,A)),join(meet(A,join(C,A)),A))) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_175,c_350]) ).
cnf(c_352,plain,
join(A,meet(meet(A,join(C,A)),A)) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_175,c_351]) ).
cnf(c_353,plain,
join(A,A) = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_117,c_352]) ).
cnf(c_354,plain,
A = meet(A,join(C,join(meet(A,B),A))),
inference(paramod,[status(thm)],[c_99,c_353]) ).
cnf(c_355,plain,
A = meet(A,join(C,A)),
inference(paramod,[status(thm)],[c_175,c_354]) ).
cnf(c_177,plain,
meet(A,join(B,A)) = A,
inference(copy,[status(thm)],[c_355]) ).
cnf(c_356,plain,
meet(join(A,B),join(C,A)) = join(A,meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_177,c_172]) ).
cnf(c_179,plain,
join(A,meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)),
inference(copy,[status(thm)],[c_356]) ).
cnf(c_180,plain,
meet(join(A,B),join(join(A,B),A)) = join(A,B),
inference(paramod,[status(thm)],[c_179,c_121]) ).
cnf(c_357,plain,
join(meet(A,join(A,B)),meet(A,join(A,B))) = A,
inference(paramod,[status(thm)],[c_180,c_126]) ).
cnf(c_181,plain,
meet(A,join(A,B)) = A,
inference(paramod,[status(thm)],[c_99,c_357]) ).
cnf(c_358,plain,
join(meet(meet(A,B),A),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_181,c_140]) ).
cnf(c_186,plain,
meet(meet(A,B),A) = meet(A,B),
inference(paramod,[status(thm)],[c_99,c_358]) ).
cnf(c_359,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_181,c_32]) ).
cnf(c_187,plain,
meet(A,meet(join(A,B),join(C,A))) = A,
inference(paramod,[status(thm)],[c_99,c_359]) ).
cnf(c_199,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_186,c_101]) ).
cnf(c_218,plain,
meet(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_199,c_19]) ).
cnf(c_360,plain,
meet(meet(A,B),meet(B,A)) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_218,c_186]) ).
cnf(c_361,plain,
meet(B,A) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_218,c_360]) ).
cnf(c_223,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_218,c_361]) ).
cnf(c_362,plain,
( join(b,a) != join(a,b)
| meet(a,b) != meet(a,b) ),
inference(paramod,[status(thm)],[c_223,c_102]) ).
cnf(c_234,plain,
join(b,a) != join(a,b),
inference(copy,[status(thm)],[c_362]) ).
cnf(c_238,plain,
meet(A,meet(join(B,A),join(A,C))) = A,
inference(paramod,[status(thm)],[c_223,c_187]) ).
cnf(c_363,plain,
join(join(A,B),meet(join(A,B),join(B,A))) = meet(join(A,B),join(B,A)),
inference(paramod,[status(thm)],[c_238,c_25]) ).
cnf(c_364,plain,
join(A,B) = meet(join(A,B),join(B,A)),
inference(paramod,[status(thm)],[c_199,c_363]) ).
cnf(c_303,plain,
meet(join(A,B),join(B,A)) = join(A,B),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_318,plain,
join(join(A,B),join(B,A)) = join(A,B),
inference(paramod,[status(thm)],[c_303,c_101]) ).
cnf(c_365,plain,
join(join(A,B),join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_303,c_131]) ).
cnf(c_319,plain,
join(A,B) = join(B,A),
inference(paramod,[status(thm)],[c_318,c_365]) ).
cnf(c_320,plain,
$false,
inference(resolve,[status(thm)],[c_319,c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:58:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3531535 was started by sandbox2 on n019,
% 0.09/0.35 % Fri Sep 25 19:58:18 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.47
% 0.14/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.47
% 0.14/0.47 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.14/0.47 % Length of proof is 60.
% 0.14/0.47 % Level of proof is 22.
% 0.14/0.47 % Maximum clause weight is 93.000.
% 0.14/0.47 % Given clauses 58.
% 0.14/0.47
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
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