%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT090-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:49:40 AM UTC 2026
% Result : Unsatisfiable 0.04s 0.41s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 8 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wal_absorbtion_1,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_1),meet(VAR_0,join(VAR_0,VAR_1))) = VAR_0,
file('theBenchmark.p',wal_absorbtion_1) ).
cnf(c_1,plain,
join(meet(A,B),meet(A,join(A,B))) = A,
inference(clausify,[status(thm)],[wal_absorbtion_1]) ).
fof(wal_absorbtion_2,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_0),meet(VAR_1,join(VAR_0,VAR_0))) = VAR_0,
file('theBenchmark.p',wal_absorbtion_2) ).
cnf(c_2,plain,
join(meet(A,A),meet(B,join(A,A))) = A,
inference(clausify,[status(thm)],[wal_absorbtion_2]) ).
fof(wal_absorbtion_3,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_1),meet(VAR_1,join(VAR_0,VAR_1))) = VAR_1,
file('theBenchmark.p',wal_absorbtion_3) ).
cnf(c_3,plain,
join(meet(A,B),meet(B,join(A,B))) = B,
inference(clausify,[status(thm)],[wal_absorbtion_3]) ).
fof(wal_absorbtion_4,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_2,VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',wal_absorbtion_4) ).
cnf(c_4,plain,
meet(meet(join(A,B),join(C,A)),A) = A,
inference(clausify,[status(thm)],[wal_absorbtion_4]) ).
fof(wal_absorbtion_5,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_2,VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',wal_absorbtion_5) ).
cnf(c_5,plain,
join(join(meet(A,B),meet(C,A)),A) = A,
inference(clausify,[status(thm)],[wal_absorbtion_5]) ).
fof(prove_normal_axioms_3,axiom,
join(a,a) != a,
file('theBenchmark.p',prove_normal_axioms_3) ).
cnf(c_6,plain,
join(a,a) != a,
inference(clausify,[status(thm)],[prove_normal_axioms_3]) ).
cnf(c_16,plain,
join(meet(A,A),join(A,A)) = A,
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_24,plain,
meet(meet(join(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_35,plain,
join(meet(meet(A,A),join(A,A)),meet(meet(A,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_36,plain,
join(meet(meet(A,A),join(A,A)),meet(join(A,A),A)) = join(A,A),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_40,plain,
meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_90,plain,
meet(meet(meet(join(A,B),join(C,A)),A),meet(meet(join(A,B),join(C,A)),A)) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_40]) ).
cnf(c_91,plain,
meet(A,meet(meet(join(A,B),join(C,A)),A)) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_90]) ).
cnf(c_92,plain,
meet(A,A) = meet(meet(join(A,B),join(C,A)),A),
inference(paramod,[status(thm)],[c_4,c_91]) ).
cnf(c_55,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_4,c_92]) ).
cnf(c_62,plain,
join(meet(A,join(A,A)),meet(join(A,A),A)) = join(A,A),
inference(paramod,[status(thm)],[c_55,c_36]) ).
cnf(c_93,plain,
join(meet(A,join(A,A)),meet(meet(A,A),A)) = meet(A,A),
inference(paramod,[status(thm)],[c_55,c_35]) ).
cnf(c_94,plain,
join(meet(A,join(A,A)),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_55,c_93]) ).
cnf(c_95,plain,
join(meet(A,join(A,A)),A) = meet(A,A),
inference(paramod,[status(thm)],[c_55,c_94]) ).
cnf(c_63,plain,
join(meet(A,join(A,A)),A) = A,
inference(paramod,[status(thm)],[c_55,c_95]) ).
cnf(c_85,plain,
meet(join(A,A),A) = A,
inference(paramod,[status(thm)],[c_55,c_4]) ).
cnf(c_96,plain,
join(meet(A,join(A,A)),A) = join(A,A),
inference(paramod,[status(thm)],[c_85,c_62]) ).
cnf(c_97,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_63,c_96]) ).
cnf(c_88,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT090-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.34 % Computer : n010.cluster.edu
% 0.04/0.34 % Model : x86_64 x86_64
% 0.04/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.34 % Memory : 8046.5625MB
% 0.04/0.34 % OS : Linux 6.8.0-71-generic
% 0.04/0.34 % CPULimit : 300
% 0.04/0.34 % WCLimit : 300
% 0.04/0.34 % DateTime : Fri Sep 25 20:03:46 UTC 2026
% 0.04/0.35 % CPUTime :
% 0.04/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.35 % Process 1527172 was started by sandbox on n010,
% 0.04/0.35 % Fri Sep 25 20:03:46 2026
% 0.04/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.35
% 0.04/0.35 % From the command line: assign(max_seconds, 300).
% 0.04/0.41
% 0.04/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.04/0.41
% 0.04/0.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/0.41 % Length of proof is 17.
% 0.04/0.41 % Level of proof is 6.
% 0.04/0.41 % Maximum clause weight is 17.000.
% 0.04/0.41 % Given clauses 13.
% 0.04/0.41
% 0.04/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------