%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT032-1 : 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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 51 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(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]) ).
cnf(c_10,plain,
meet(join(A,B),join(A,C)) = join(A,meet(B,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(dist_meet,axiom,
meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)),
file('theBenchmark.p',dist_meet) ).
cnf(c_11,plain,
meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)),
inference(clausify,[status(thm)],[dist_meet]) ).
cnf(c_84,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_18,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_30,plain,
meet(join(A,B),join(B,C)) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_43,plain,
meet(join(A,B),join(C,B)) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_6,c_30]) ).
cnf(c_50,plain,
meet(A,join(B,meet(A,C))) = join(meet(A,C),meet(A,B)),
inference(paramod,[status(thm)],[c_4,c_43]) ).
cnf(c_85,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_30,c_18]) ).
cnf(c_86,plain,
join(meet(A,C),meet(A,B)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_50,c_85]) ).
cnf(c_73,plain,
meet(A,join(B,C)) = join(meet(A,C),meet(A,B)),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
join(meet(xx,zz),meet(xx,yy)) != join(meet(xx,yy),meet(xx,zz)),
inference(paramod,[status(thm)],[c_73,c_11]) ).
cnf(c_88,plain,
join(meet(xx,yy),meet(xx,zz)) != join(meet(xx,yy),meet(xx,zz)),
inference(paramod,[status(thm)],[c_6,c_87]) ).
cnf(c_83,plain,
$false,
inference(copy,[status(thm)],[c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT032-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Sep 25 19:57:55 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3597425 was started by sandbox2 on n006,
% 0.13/0.36 % Fri Sep 25 19:57:55 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.39 % Length of proof is 13.
% 0.13/0.39 % Level of proof is 6.
% 0.13/0.39 % Maximum clause weight is 36.000.
% 0.13/0.39 % Given clauses 20.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------