%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT028-1 : 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 : n014.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 2.06s 0.68s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 28 sgn 20 !; 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(wal_1,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_1) ).
cnf(c_5,plain,
meet(meet(join(A,B),join(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_1]) ).
cnf(c_6,plain,
meet(A,meet(join(B,A),join(C,A))) = A,
inference(paramod,[status(thm)],[c_3,c_5]) ).
fof(wal_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_2) ).
cnf(c_7,plain,
join(join(meet(A,B),meet(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_2]) ).
cnf(c_8,plain,
join(A,join(meet(B,A),meet(C,A))) = A,
inference(paramod,[status(thm)],[c_4,c_7]) ).
fof(commutativity_of_meet2,axiom,
! [VAR_0,VAR_1] : meet2(VAR_0,VAR_1) = meet2(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet2) ).
cnf(c_10,plain,
meet2(A,B) = meet2(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet2]) ).
fof(wal_1_2,axiom,
! [VAR_0,VAR_1,VAR_2] : meet2(meet2(join(VAR_0,VAR_1),join(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_1_2) ).
cnf(c_11,plain,
meet2(meet2(join(A,B),join(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_1_2]) ).
cnf(c_12,plain,
meet2(A,meet2(join(B,A),join(C,A))) = A,
inference(paramod,[status(thm)],[c_10,c_11]) ).
fof(wal_2_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet2(VAR_0,VAR_1),meet2(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_2_2) ).
cnf(c_13,plain,
join(join(meet2(A,B),meet2(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_2_2]) ).
cnf(c_14,plain,
join(A,join(meet2(B,A),meet2(C,A))) = A,
inference(paramod,[status(thm)],[c_4,c_13]) ).
fof(name,axiom,
meet(a,b) != meet2(a,b),
file('theBenchmark.p',name) ).
cnf(c_15,plain,
meet(a,b) != meet2(a,b),
inference(clausify,[status(thm)],[name]) ).
cnf(c_16,plain,
meet2(a,b) != meet(a,b),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_22,plain,
join(A,join(meet(A,B),meet(C,A))) = A,
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_29,plain,
meet2(join(meet(A,B),meet(C,B)),meet2(B,join(D,join(meet(A,B),meet(C,B))))) = join(meet(A,B),meet(C,B)),
inference(paramod,[status(thm)],[c_8,c_12]) ).
cnf(c_31,plain,
join(A,meet2(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_14]) ).
cnf(c_32,plain,
meet(join(meet2(A,B),meet2(C,B)),meet(B,join(D,join(meet2(A,B),meet2(C,B))))) = join(meet2(A,B),meet2(C,B)),
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_33,plain,
join(A,join(meet2(A,B),meet2(C,A))) = A,
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_407,plain,
meet(meet2(A,B),B) = meet2(A,B),
inference(paramod,[status(thm)],[c_31,c_17]) ).
cnf(c_56,plain,
meet(A,meet2(B,A)) = meet2(B,A),
inference(paramod,[status(thm)],[c_3,c_407]) ).
cnf(c_91,plain,
join(A,join(meet(A,B),meet(A,C))) = A,
inference(paramod,[status(thm)],[c_3,c_22]) ).
cnf(c_168,plain,
join(A,join(meet2(A,B),meet2(A,C))) = A,
inference(paramod,[status(thm)],[c_10,c_33]) ).
cnf(c_408,plain,
meet2(join(meet(A,B),meet(A,B)),meet2(B,A)) = join(meet(A,B),meet(A,B)),
inference(paramod,[status(thm)],[c_91,c_29]) ).
cnf(c_409,plain,
meet2(meet(A,B),meet2(B,A)) = join(meet(A,B),meet(A,B)),
inference(paramod,[status(thm)],[c_2,c_408]) ).
cnf(c_349,plain,
meet2(meet(A,B),meet2(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_2,c_409]) ).
cnf(c_410,plain,
meet(meet2(A,B),meet(B,A)) = meet2(meet(B,A),meet2(A,B)),
inference(paramod,[status(thm)],[c_349,c_56]) ).
cnf(c_411,plain,
meet(meet(B,A),meet2(A,B)) = meet2(meet(B,A),meet2(A,B)),
inference(paramod,[status(thm)],[c_3,c_410]) ).
cnf(c_363,plain,
meet(meet(A,B),meet2(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_349,c_411]) ).
cnf(c_412,plain,
meet(join(meet2(A,B),meet2(A,B)),meet(B,A)) = join(meet2(A,B),meet2(A,B)),
inference(paramod,[status(thm)],[c_168,c_32]) ).
cnf(c_413,plain,
meet(meet2(A,B),meet(B,A)) = join(meet2(A,B),meet2(A,B)),
inference(paramod,[status(thm)],[c_2,c_412]) ).
cnf(c_414,plain,
meet(meet(B,A),meet2(A,B)) = join(meet2(A,B),meet2(A,B)),
inference(paramod,[status(thm)],[c_3,c_413]) ).
cnf(c_415,plain,
meet(B,A) = join(meet2(A,B),meet2(A,B)),
inference(paramod,[status(thm)],[c_363,c_414]) ).
cnf(c_416,plain,
meet(B,A) = meet2(A,B),
inference(paramod,[status(thm)],[c_2,c_415]) ).
cnf(c_397,plain,
meet2(A,B) = meet(B,A),
inference(copy,[status(thm)],[c_416]) ).
cnf(c_417,plain,
meet(b,a) != meet(a,b),
inference(paramod,[status(thm)],[c_397,c_16]) ).
cnf(c_418,plain,
meet(a,b) != meet(a,b),
inference(paramod,[status(thm)],[c_3,c_417]) ).
cnf(c_406,plain,
$false,
inference(copy,[status(thm)],[c_418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 19:57:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 961763 was started by sandbox2 on n014,
% 0.08/0.35 % Fri Sep 25 19:57:47 2026
% 0.08/0.35 % 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).
% 2.06/0.68
% 2.06/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.06/0.68
% 2.06/0.68 % Proof 1 at 0.24 (+ 0.07) seconds.
% 2.06/0.68 % Length of proof is 28.
% 2.06/0.68 % Level of proof is 7.
% 2.06/0.68 % Maximum clause weight is 67.000.
% 2.06/0.68 % Given clauses 68.
% 2.06/0.68
% 2.06/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------