%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT021-1 : 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 : 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 07:49:33 AM UTC 2026
% Result : Unsatisfiable 0.94s 0.61s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 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 : 131 ( 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(bowden,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(VAR_0,meet(VAR_1,VAR_2)),meet(join(VAR_0,VAR_1),VAR_2)) = join(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',bowden) ).
cnf(c_11,plain,
join(join(A,meet(B,C)),meet(join(A,B),C)) = join(A,meet(B,C)),
inference(clausify,[status(thm)],[bowden]) ).
cnf(c_12,plain,
join(A,join(meet(B,C),meet(join(A,B),C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_6,c_11]) ).
fof(prove_distributivity,axiom,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_13,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_186,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_16,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_3,c_186]) ).
cnf(c_187,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_187]) ).
cnf(c_188,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_188]) ).
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_33,plain,
meet(join(A,B),join(meet(B,C),A)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_4,c_10]) ).
cnf(c_40,plain,
join(A,join(meet(B,C),meet(C,join(A,B)))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_12]) ).
cnf(c_45,plain,
join(meet(A,B),meet(B,join(meet(A,B),C))) = meet(B,join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_189,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_85,plain,
join(meet(A,join(B,C)),meet(B,A)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_190,plain,
join(meet(A,B),meet(B,join(C,A))) = meet(B,join(A,join(C,A))),
inference(paramod,[status(thm)],[c_21,c_26]) ).
cnf(c_88,plain,
join(meet(A,B),meet(B,join(C,A))) = meet(B,join(C,A)),
inference(paramod,[status(thm)],[c_21,c_190]) ).
cnf(c_89,plain,
join(A,meet(B,join(A,C))) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_88,c_40]) ).
cnf(c_100,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_89]) ).
cnf(c_191,plain,
join(meet(A,B),meet(B,C)) = meet(B,join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_100,c_45]) ).
cnf(c_116,plain,
meet(A,join(meet(B,A),C)) = join(meet(B,A),meet(A,C)),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_192,plain,
meet(join(meet(A,join(B,C)),B),meet(A,join(B,C))) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_26,c_33]) ).
cnf(c_193,plain,
meet(join(B,meet(A,join(B,C))),meet(A,join(B,C))) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_4,c_192]) ).
cnf(c_194,plain,
meet(join(B,meet(A,C)),meet(A,join(B,C))) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_100,c_193]) ).
cnf(c_195,plain,
meet(A,meet(join(B,meet(A,C)),join(B,C))) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_18,c_194]) ).
cnf(c_196,plain,
meet(A,meet(join(B,C),join(B,meet(A,C)))) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_3,c_195]) ).
cnf(c_197,plain,
meet(A,join(B,meet(C,A))) = join(meet(A,join(B,C)),meet(B,A)),
inference(paramod,[status(thm)],[c_31,c_196]) ).
cnf(c_157,plain,
meet(A,join(B,meet(C,A))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_85,c_197]) ).
cnf(c_198,plain,
meet(A,join(meet(B,A),C)) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_4,c_157]) ).
cnf(c_170,plain,
join(meet(A,B),meet(B,C)) = meet(B,join(C,A)),
inference(paramod,[status(thm)],[c_116,c_198]) ).
cnf(c_199,plain,
join(meet(c,a),meet(a,b)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_170,c_13]) ).
cnf(c_200,plain,
join(meet(a,c),meet(a,b)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_3,c_199]) ).
cnf(c_201,plain,
join(meet(a,b),meet(a,c)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_4,c_200]) ).
cnf(c_185,plain,
$false,
inference(copy,[status(thm)],[c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT021-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 20:00:27 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2106898 was started by sandbox2 on n015,
% 0.17/0.44 % Fri Sep 25 20:00:27 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.94/0.61
% 0.94/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.94/0.61
% 0.94/0.61 % Proof 1 at 0.11 (+ 0.04) seconds.
% 0.94/0.61 % Length of proof is 29.
% 0.94/0.61 % Level of proof is 8.
% 0.94/0.61 % Maximum clause weight is 29.000.
% 0.94/0.61 % Given clauses 45.
% 0.94/0.61
% 0.94/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------