%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT031-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 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 : 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 : 96 ( 3 sgn 19 !; 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(absorption1,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1) ).
cnf(c_3,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1]) ).
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(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_7,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_8,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_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_9,plain,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[dist_meet]) ).
cnf(c_10,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(dist_join,axiom,
join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)),
file('theBenchmark.p',dist_join) ).
cnf(c_11,plain,
join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)),
inference(clausify,[status(thm)],[dist_join]) ).
cnf(c_12,plain,
meet(join(xx,yy),join(xx,zz)) != join(xx,meet(yy,zz)),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_117,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_16,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_118,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_24,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_118]) ).
cnf(c_119,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_29,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_119]) ).
cnf(c_31,plain,
join(meet(A,B),meet(B,C)) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_42,plain,
join(meet(A,B),meet(C,B)) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_5,c_31]) ).
cnf(c_51,plain,
join(A,meet(B,join(A,C))) = meet(join(A,C),join(A,B)),
inference(paramod,[status(thm)],[c_3,c_42]) ).
cnf(c_120,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(B,meet(A,C))),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_121,plain,
meet(A,join(B,C)) = meet(A,join(B,meet(A,C))),
inference(paramod,[status(thm)],[c_10,c_120]) ).
cnf(c_61,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_122,plain,
join(join(A,meet(B,C)),meet(B,join(A,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_61,c_13]) ).
cnf(c_123,plain,
join(meet(B,join(A,C)),join(A,meet(B,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_6,c_122]) ).
cnf(c_124,plain,
join(A,join(meet(B,join(A,C)),meet(B,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_29,c_123]) ).
cnf(c_125,plain,
join(A,join(meet(B,C),meet(B,join(A,C)))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_6,c_124]) ).
cnf(c_126,plain,
join(A,meet(B,join(C,join(A,C)))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_10,c_125]) ).
cnf(c_127,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_24,c_126]) ).
cnf(c_108,plain,
meet(join(A,B),join(A,C)) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_51,c_127]) ).
cnf(c_128,plain,
join(xx,meet(zz,yy)) != join(xx,meet(yy,zz)),
inference(paramod,[status(thm)],[c_108,c_12]) ).
cnf(c_129,plain,
join(xx,meet(yy,zz)) != join(xx,meet(yy,zz)),
inference(paramod,[status(thm)],[c_5,c_128]) ).
cnf(c_116,plain,
$false,
inference(copy,[status(thm)],[c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT031-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n007.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 19:56:08 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 1737821 was started by sandbox on n007,
% 0.17/0.44 % Fri Sep 25 19:56:08 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.48 % Length of proof is 22.
% 0.17/0.48 % Level of proof is 6.
% 0.17/0.48 % Maximum clause weight is 36.000.
% 0.17/0.48 % Given clauses 24.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------