%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT038-1 : 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 : n006.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 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn 13 !; 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(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_4,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption2]) ).
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_meet,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)),
file('theBenchmark.p',dist_meet) ).
cnf(c_11,plain,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[dist_meet]) ).
fof(f_on_left_join,axiom,
! [VAR_0,VAR_1,VAR_2] : f(join(VAR_0,VAR_1),VAR_2) = join(f(VAR_0,VAR_2),f(VAR_1,VAR_2)),
file('theBenchmark.p',f_on_left_join) ).
cnf(c_12,plain,
f(join(A,B),C) = join(f(A,C),f(B,C)),
inference(clausify,[status(thm)],[f_on_left_join]) ).
fof(lhs1,axiom,
f(join(aa,bb),dd) = f(join(cc,bb),dd),
file('theBenchmark.p',lhs1) ).
cnf(c_16,plain,
f(join(aa,bb),dd) = f(join(cc,bb),dd),
inference(clausify,[status(thm)],[lhs1]) ).
cnf(c_219,plain,
f(join(bb,aa),dd) = f(join(cc,bb),dd),
inference(paramod,[status(thm)],[c_6,c_16]) ).
cnf(c_220,plain,
join(f(bb,dd),f(aa,dd)) = f(join(cc,bb),dd),
inference(paramod,[status(thm)],[c_12,c_219]) ).
cnf(c_221,plain,
join(f(bb,dd),f(aa,dd)) = f(join(bb,cc),dd),
inference(paramod,[status(thm)],[c_6,c_220]) ).
cnf(c_222,plain,
join(f(bb,dd),f(aa,dd)) = join(f(bb,dd),f(cc,dd)),
inference(paramod,[status(thm)],[c_12,c_221]) ).
cnf(c_17,plain,
join(f(bb,dd),f(cc,dd)) = join(f(bb,dd),f(aa,dd)),
inference(copy,[status(thm)],[c_222]) ).
fof(lhs2,axiom,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)),
file('theBenchmark.p',lhs2) ).
cnf(c_18,plain,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)),
inference(clausify,[status(thm)],[lhs2]) ).
cnf(c_223,plain,
meet(f(bb,dd),f(aa,dd)) = meet(f(cc,dd),f(bb,dd)),
inference(paramod,[status(thm)],[c_5,c_18]) ).
cnf(c_224,plain,
meet(f(bb,dd),f(aa,dd)) = meet(f(bb,dd),f(cc,dd)),
inference(paramod,[status(thm)],[c_5,c_223]) ).
cnf(c_19,plain,
meet(f(bb,dd),f(cc,dd)) = meet(f(bb,dd),f(aa,dd)),
inference(copy,[status(thm)],[c_224]) ).
fof(rhs,axiom,
f(aa,dd) != f(cc,dd),
file('theBenchmark.p',rhs) ).
cnf(c_20,plain,
f(aa,dd) != f(cc,dd),
inference(clausify,[status(thm)],[rhs]) ).
cnf(c_21,plain,
f(cc,dd) != f(aa,dd),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_23,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_225,plain,
meet(A,join(f(bb,dd),f(aa,dd))) = join(meet(A,f(bb,dd)),meet(A,f(cc,dd))),
inference(paramod,[status(thm)],[c_17,c_11]) ).
cnf(c_226,plain,
join(meet(A,f(bb,dd)),meet(A,f(aa,dd))) = join(meet(A,f(bb,dd)),meet(A,f(cc,dd))),
inference(paramod,[status(thm)],[c_11,c_225]) ).
cnf(c_42,plain,
join(meet(A,f(bb,dd)),meet(A,f(cc,dd))) = join(meet(A,f(bb,dd)),meet(A,f(aa,dd))),
inference(copy,[status(thm)],[c_226]) ).
cnf(c_227,plain,
join(f(cc,dd),meet(f(bb,dd),f(aa,dd))) = f(cc,dd),
inference(paramod,[status(thm)],[c_19,c_23]) ).
cnf(c_62,plain,
join(meet(f(bb,dd),f(aa,dd)),f(cc,dd)) = f(cc,dd),
inference(paramod,[status(thm)],[c_6,c_227]) ).
cnf(c_228,plain,
join(meet(f(cc,dd),f(bb,dd)),f(cc,dd)) = join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_229,plain,
join(meet(f(bb,dd),f(cc,dd)),f(cc,dd)) = join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_5,c_228]) ).
cnf(c_230,plain,
join(meet(f(bb,dd),f(aa,dd)),f(cc,dd)) = join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_19,c_229]) ).
cnf(c_231,plain,
f(cc,dd) = join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_62,c_230]) ).
cnf(c_232,plain,
f(cc,dd) = join(meet(f(bb,dd),f(cc,dd)),meet(f(cc,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_5,c_231]) ).
cnf(c_233,plain,
f(cc,dd) = join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_19,c_232]) ).
cnf(c_234,plain,
f(cc,dd) = join(meet(f(bb,dd),f(aa,dd)),meet(f(aa,dd),f(cc,dd))),
inference(paramod,[status(thm)],[c_5,c_233]) ).
cnf(c_216,plain,
join(meet(f(bb,dd),f(aa,dd)),meet(f(aa,dd),f(cc,dd))) = f(cc,dd),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_235,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))) = join(meet(f(aa,dd),f(bb,dd)),f(aa,dd)),
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_236,plain,
join(meet(f(bb,dd),f(aa,dd)),meet(f(aa,dd),f(cc,dd))) = join(meet(f(aa,dd),f(bb,dd)),f(aa,dd)),
inference(paramod,[status(thm)],[c_5,c_235]) ).
cnf(c_237,plain,
f(cc,dd) = join(meet(f(aa,dd),f(bb,dd)),f(aa,dd)),
inference(paramod,[status(thm)],[c_216,c_236]) ).
cnf(c_238,plain,
f(cc,dd) = join(meet(f(bb,dd),f(aa,dd)),f(aa,dd)),
inference(paramod,[status(thm)],[c_5,c_237]) ).
cnf(c_239,plain,
f(cc,dd) = join(f(aa,dd),meet(f(bb,dd),f(aa,dd))),
inference(paramod,[status(thm)],[c_6,c_238]) ).
cnf(c_217,plain,
f(cc,dd) = f(aa,dd),
inference(paramod,[status(thm)],[c_23,c_239]) ).
cnf(c_218,plain,
$false,
inference(resolve,[status(thm)],[c_217,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT038-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:58:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3598245 was started by sandbox2 on n006,
% 0.09/0.37 % Fri Sep 25 19:58:41 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.41
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.41 % Length of proof is 18.
% 0.09/0.41 % Level of proof is 5.
% 0.09/0.41 % Maximum clause weight is 43.000.
% 0.09/0.41 % Given clauses 37.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------