%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT023-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 6.20s 1.31s
% Output : CNFRefutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 98 ( 98 unt; 0 def)
% Number of atoms : 98 ( 97 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 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 : 248 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_1,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
fof(idempotence_of_join,axiom,
! [VAR_0] : join(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_join) ).
cnf(c_2,plain,
join(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_join]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_3,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(commutativity_of_join,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_4,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(associativity_of_meet,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(VAR_0,VAR_1),VAR_2) = meet(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_meet) ).
cnf(c_5,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(clausify,[status(thm)],[associativity_of_meet]) ).
fof(associativity_of_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(VAR_0,VAR_1),VAR_2) = join(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_join) ).
cnf(c_6,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(quasi_lattice1,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(VAR_0,join(VAR_1,VAR_2)),meet(VAR_0,VAR_1)) = meet(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',quasi_lattice1) ).
cnf(c_7,plain,
join(meet(A,join(B,C)),meet(A,B)) = meet(A,join(B,C)),
inference(clausify,[status(thm)],[quasi_lattice1]) ).
cnf(c_8,plain,
join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_4,c_7]) ).
fof(quasi_lattice2,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(join(VAR_0,meet(VAR_1,VAR_2)),join(VAR_0,VAR_1)) = join(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',quasi_lattice2) ).
cnf(c_9,plain,
meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)),
inference(clausify,[status(thm)],[quasi_lattice2]) ).
cnf(c_10,plain,
meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_9]) ).
fof(modularity_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(join(VAR_0,VAR_1),VAR_2),VAR_1) = join(meet(join(VAR_2,VAR_1),VAR_0),VAR_1),
file('theBenchmark.p',modularity_axiom) ).
cnf(c_11,plain,
join(meet(join(A,B),C),B) = join(meet(join(C,B),A),B),
inference(clausify,[status(thm)],[modularity_axiom]) ).
cnf(c_339,plain,
join(B,meet(join(A,B),C)) = join(meet(join(C,B),A),B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_12,plain,
join(A,meet(join(B,A),C)) = join(A,meet(join(C,A),B)),
inference(paramod,[status(thm)],[c_4,c_339]) ).
fof(prove_modularity,axiom,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
file('theBenchmark.p',prove_modularity) ).
cnf(c_13,plain,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
inference(clausify,[status(thm)],[prove_modularity]) ).
cnf(c_340,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_15,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_340]) ).
cnf(c_341,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_18,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_341]) ).
cnf(c_342,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_20,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_342]) ).
cnf(c_343,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_21,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_4,c_343]) ).
cnf(c_344,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_23,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_344]) ).
cnf(c_24,plain,
join(A,meet(A,join(A,B))) = meet(A,join(A,B)),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_26,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_31,plain,
meet(join(A,B),join(A,meet(C,B))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_345,plain,
meet(join(meet(A,B),A),meet(A,join(B,C))) = join(meet(A,B),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_346,plain,
meet(join(A,meet(A,B)),meet(A,join(B,C))) = join(meet(A,B),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_4,c_345]) ).
cnf(c_347,plain,
meet(A,meet(join(A,meet(A,B)),join(B,C))) = join(meet(A,B),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_18,c_346]) ).
cnf(c_35,plain,
meet(A,meet(join(A,meet(A,B)),join(B,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_8,c_347]) ).
cnf(c_348,plain,
join(A,meet(A,B)) = join(A,meet(join(B,A),A)),
inference(paramod,[status(thm)],[c_2,c_12]) ).
cnf(c_349,plain,
join(A,meet(A,B)) = join(A,meet(A,join(B,A))),
inference(paramod,[status(thm)],[c_3,c_348]) ).
cnf(c_37,plain,
join(A,meet(A,join(B,A))) = join(A,meet(A,B)),
inference(copy,[status(thm)],[c_349]) ).
cnf(c_350,plain,
join(A,meet(B,join(C,A))) = join(A,meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_3,c_12]) ).
cnf(c_38,plain,
join(A,meet(join(B,A),C)) = join(A,meet(B,join(C,A))),
inference(copy,[status(thm)],[c_350]) ).
cnf(c_351,plain,
meet(join(A,join(B,A)),join(A,meet(join(C,A),B))) = join(A,meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_352,plain,
meet(join(B,A),join(A,meet(join(C,A),B))) = join(A,meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_21,c_351]) ).
cnf(c_353,plain,
meet(join(B,A),join(A,meet(C,join(B,A)))) = join(A,meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_38,c_352]) ).
cnf(c_41,plain,
meet(join(A,B),join(B,meet(C,join(A,B)))) = join(B,meet(A,join(C,B))),
inference(paramod,[status(thm)],[c_38,c_353]) ).
cnf(c_354,plain,
join(meet(A,B),meet(A,join(C,B))) = meet(A,join(B,join(C,B))),
inference(paramod,[status(thm)],[c_21,c_8]) ).
cnf(c_49,plain,
join(meet(A,B),meet(A,join(C,B))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_21,c_354]) ).
cnf(c_355,plain,
join(A,meet(A,join(B,A))) = meet(A,join(A,B)),
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_356,plain,
join(A,meet(A,B)) = meet(A,join(A,B)),
inference(paramod,[status(thm)],[c_37,c_355]) ).
cnf(c_62,plain,
meet(A,join(A,B)) = join(A,meet(A,B)),
inference(copy,[status(thm)],[c_356]) ).
cnf(c_357,plain,
join(A,meet(A,join(A,B))) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_358,plain,
join(A,join(A,meet(A,B))) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_62,c_357]) ).
cnf(c_359,plain,
join(A,meet(A,B)) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_20,c_358]) ).
cnf(c_63,plain,
meet(A,join(B,A)) = join(A,meet(A,B)),
inference(copy,[status(thm)],[c_359]) ).
cnf(c_69,plain,
meet(join(A,meet(A,B)),C) = meet(A,meet(join(A,B),C)),
inference(paramod,[status(thm)],[c_62,c_5]) ).
cnf(c_360,plain,
meet(A,meet(A,meet(join(A,B),join(B,C)))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_69,c_35]) ).
cnf(c_71,plain,
meet(A,meet(join(A,B),join(B,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_15,c_360]) ).
cnf(c_72,plain,
meet(A,join(B,join(C,A))) = join(A,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_6,c_63]) ).
cnf(c_361,plain,
join(meet(A,B),meet(B,A)) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_2,c_26]) ).
cnf(c_80,plain,
join(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_2,c_361]) ).
cnf(c_362,plain,
meet(A,join(B,C)) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_26,c_4]) ).
cnf(c_82,plain,
join(meet(A,join(B,C)),meet(B,A)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_362]) ).
cnf(c_94,plain,
meet(join(A,B),join(B,meet(C,A))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_4,c_31]) ).
cnf(c_95,plain,
meet(join(A,B),join(meet(C,B),A)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_4,c_31]) ).
cnf(c_116,plain,
join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_15,c_49]) ).
cnf(c_363,plain,
join(join(A,meet(B,C)),meet(A,join(A,B))) = meet(join(A,B),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_10,c_82]) ).
cnf(c_364,plain,
join(join(A,meet(B,C)),join(A,meet(A,B))) = meet(join(A,B),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_62,c_363]) ).
cnf(c_365,plain,
join(A,join(join(A,meet(B,C)),meet(A,B))) = meet(join(A,B),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_23,c_364]) ).
cnf(c_366,plain,
join(A,join(A,join(meet(B,C),meet(A,B)))) = meet(join(A,B),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_6,c_365]) ).
cnf(c_367,plain,
join(A,join(meet(B,C),meet(A,B))) = meet(join(A,B),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_20,c_366]) ).
cnf(c_129,plain,
join(A,join(meet(B,C),meet(A,B))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_10,c_367]) ).
cnf(c_368,plain,
join(A,meet(B,C)) = meet(join(meet(C,B),A),join(A,B)),
inference(paramod,[status(thm)],[c_95,c_3]) ).
cnf(c_146,plain,
meet(join(meet(A,B),C),join(C,B)) = join(C,meet(B,A)),
inference(copy,[status(thm)],[c_368]) ).
cnf(c_369,plain,
meet(meet(A,B),join(C,meet(B,A))) = meet(meet(A,B),join(C,B)),
inference(paramod,[status(thm)],[c_146,c_71]) ).
cnf(c_370,plain,
meet(A,meet(B,join(C,meet(B,A)))) = meet(meet(A,B),join(C,B)),
inference(paramod,[status(thm)],[c_5,c_369]) ).
cnf(c_371,plain,
meet(A,meet(B,join(C,meet(B,A)))) = meet(A,meet(B,join(C,B))),
inference(paramod,[status(thm)],[c_5,c_370]) ).
cnf(c_286,plain,
meet(A,meet(B,join(C,meet(B,A)))) = meet(A,join(B,meet(B,C))),
inference(paramod,[status(thm)],[c_63,c_371]) ).
cnf(c_372,plain,
meet(meet(A,B),join(C,meet(A,B))) = join(meet(A,B),meet(meet(A,B),join(C,meet(B,A)))),
inference(paramod,[status(thm)],[c_80,c_72]) ).
cnf(c_373,plain,
join(meet(A,B),meet(meet(A,B),C)) = join(meet(A,B),meet(meet(A,B),join(C,meet(B,A)))),
inference(paramod,[status(thm)],[c_63,c_372]) ).
cnf(c_374,plain,
join(meet(A,B),meet(A,meet(B,C))) = join(meet(A,B),meet(meet(A,B),join(C,meet(B,A)))),
inference(paramod,[status(thm)],[c_5,c_373]) ).
cnf(c_375,plain,
join(meet(A,B),meet(A,meet(B,C))) = join(meet(A,B),meet(A,meet(B,join(C,meet(B,A))))),
inference(paramod,[status(thm)],[c_5,c_374]) ).
cnf(c_376,plain,
join(meet(A,B),meet(A,meet(B,C))) = join(meet(A,B),meet(A,join(B,meet(B,C)))),
inference(paramod,[status(thm)],[c_286,c_375]) ).
cnf(c_377,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,join(B,meet(B,C))),
inference(paramod,[status(thm)],[c_8,c_376]) ).
cnf(c_289,plain,
meet(A,join(B,meet(B,C))) = join(meet(A,B),meet(A,meet(B,C))),
inference(copy,[status(thm)],[c_377]) ).
cnf(c_316,plain,
join(A,join(meet(B,C),meet(B,A))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_129]) ).
cnf(c_378,plain,
meet(join(A,meet(A,B)),join(meet(A,B),meet(C,join(A,meet(A,B))))) = meet(A,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_116,c_41]) ).
cnf(c_379,plain,
meet(join(A,meet(A,B)),join(meet(A,B),join(meet(C,A),meet(C,meet(A,B))))) = meet(A,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_289,c_378]) ).
cnf(c_380,plain,
meet(join(A,meet(A,B)),join(meet(A,B),meet(C,A))) = meet(A,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_316,c_379]) ).
cnf(c_381,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_94,c_380]) ).
cnf(c_334,plain,
meet(A,join(B,meet(A,C))) = join(meet(A,C),meet(A,B)),
inference(copy,[status(thm)],[c_381]) ).
cnf(c_382,plain,
join(meet(a,c),meet(a,b)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_334,c_13]) ).
cnf(c_383,plain,
join(meet(a,b),meet(a,c)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_4,c_382]) ).
cnf(c_338,plain,
$false,
inference(copy,[status(thm)],[c_383]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT023-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.51 % Computer : n004.cluster.edu
% 0.10/0.51 % Model : x86_64 x86_64
% 0.10/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.51 % Memory : 8046.5625MB
% 0.10/0.51 % OS : Linux 6.8.0-71-generic
% 0.10/0.51 % CPULimit : 300
% 0.10/0.51 % WCLimit : 300
% 0.10/0.51 % DateTime : Fri Sep 25 19:57:22 UTC 2026
% 0.10/0.51 % CPUTime :
% 0.10/0.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.51 % Process 3948546 was started by sandbox on n004,
% 0.10/0.51 % Fri Sep 25 19:57:22 2026
% 0.10/0.51 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.52
% 0.10/0.52 % From the command line: assign(max_seconds, 300).
% 6.20/1.31
% 6.20/1.31 % SZS status Unsatisfiable for theBenchmark
% 6.20/1.31
% 6.20/1.31 % Proof 1 at 0.60 (+ 0.18) seconds.
% 6.20/1.31 % Length of proof is 43.
% 6.20/1.31 % Level of proof is 9.
% 6.20/1.31 % Maximum clause weight is 29.000.
% 6.20/1.31 % Given clauses 103.
% 6.20/1.31
% 6.20/1.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------