%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:49:35 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_5,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_6,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(dist_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,meet(VAR_1,VAR_2)) = meet(join(VAR_0,VAR_1),join(VAR_0,VAR_2)),
file('theBenchmark.p',dist_join) ).
cnf(c_9,plain,
join(A,meet(B,C)) = meet(join(A,B),join(A,C)),
inference(clausify,[status(thm)],[dist_join]) ).
fof(x_join_0,axiom,
! [VAR_0] : join(VAR_0,n0) = VAR_0,
file('theBenchmark.p',x_join_0) ).
cnf(c_13,plain,
join(A,n0) = A,
inference(clausify,[status(thm)],[x_join_0]) ).
fof(x_meet_1,axiom,
! [VAR_0] : meet(VAR_0,n1) = VAR_0,
file('theBenchmark.p',x_meet_1) ).
cnf(c_14,plain,
meet(A,n1) = A,
inference(clausify,[status(thm)],[x_meet_1]) ).
fof(lhs1,axiom,
join(xx,yy) = n1,
file('theBenchmark.p',lhs1) ).
cnf(c_18,plain,
join(xx,yy) = n1,
inference(clausify,[status(thm)],[lhs1]) ).
fof(lhs2,axiom,
join(xx,zz) = n1,
file('theBenchmark.p',lhs2) ).
cnf(c_19,plain,
join(xx,zz) = n1,
inference(clausify,[status(thm)],[lhs2]) ).
fof(lhs3,axiom,
meet(xx,yy) = n0,
file('theBenchmark.p',lhs3) ).
cnf(c_20,plain,
meet(xx,yy) = n0,
inference(clausify,[status(thm)],[lhs3]) ).
fof(lhs4,axiom,
meet(xx,zz) = n0,
file('theBenchmark.p',lhs4) ).
cnf(c_21,plain,
meet(xx,zz) = n0,
inference(clausify,[status(thm)],[lhs4]) ).
fof(rhs,axiom,
yy != zz,
file('theBenchmark.p',rhs) ).
cnf(c_22,plain,
yy != zz,
inference(clausify,[status(thm)],[rhs]) ).
cnf(c_23,plain,
zz != yy,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_134,plain,
A = meet(n1,A),
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_49,plain,
meet(n1,A) = A,
inference(copy,[status(thm)],[c_134]) ).
cnf(c_135,plain,
join(A,n0) = meet(join(A,xx),join(A,yy)),
inference(paramod,[status(thm)],[c_20,c_9]) ).
cnf(c_136,plain,
A = meet(join(A,xx),join(A,yy)),
inference(paramod,[status(thm)],[c_13,c_135]) ).
cnf(c_61,plain,
meet(join(A,xx),join(A,yy)) = A,
inference(copy,[status(thm)],[c_136]) ).
cnf(c_137,plain,
join(A,n0) = meet(join(A,xx),join(A,zz)),
inference(paramod,[status(thm)],[c_21,c_9]) ).
cnf(c_138,plain,
A = meet(join(A,xx),join(A,zz)),
inference(paramod,[status(thm)],[c_13,c_137]) ).
cnf(c_66,plain,
meet(join(A,xx),join(A,zz)) = A,
inference(copy,[status(thm)],[c_138]) ).
cnf(c_78,plain,
meet(join(xx,A),join(A,yy)) = A,
inference(paramod,[status(thm)],[c_6,c_61]) ).
cnf(c_139,plain,
meet(n1,join(zz,yy)) = zz,
inference(paramod,[status(thm)],[c_19,c_78]) ).
cnf(c_140,plain,
meet(n1,join(yy,zz)) = zz,
inference(paramod,[status(thm)],[c_6,c_139]) ).
cnf(c_126,plain,
join(yy,zz) = zz,
inference(paramod,[status(thm)],[c_49,c_140]) ).
cnf(c_141,plain,
meet(join(yy,xx),zz) = yy,
inference(paramod,[status(thm)],[c_126,c_66]) ).
cnf(c_142,plain,
meet(join(xx,yy),zz) = yy,
inference(paramod,[status(thm)],[c_6,c_141]) ).
cnf(c_143,plain,
meet(n1,zz) = yy,
inference(paramod,[status(thm)],[c_18,c_142]) ).
cnf(c_132,plain,
zz = yy,
inference(paramod,[status(thm)],[c_49,c_143]) ).
cnf(c_133,plain,
$false,
inference(resolve,[status(thm)],[c_132,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 19:56:39 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1739191 was started by sandbox2 on n007,
% 0.17/0.45 % Fri Sep 25 19:56:39 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.22/0.50
% 0.22/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.50
% 0.22/0.50 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.22/0.50 % Length of proof is 18.
% 0.22/0.50 % Level of proof is 5.
% 0.22/0.50 % Maximum clause weight is 28.000.
% 0.22/0.50 % Given clauses 35.
% 0.22/0.50
% 0.22/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------