%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP182-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:28:16 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.44s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(prove_p17b,axiom,
greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity,
file('theBenchmark.p',prove_p17b) ).
cnf(c_22,plain,
greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity,
inference(clausify,[status(thm)],[prove_p17b]) ).
cnf(c_24,plain,
greatest_lower_bound(identity,least_upper_bound(identity,a)) != identity,
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_25,plain,
identity != identity,
inference(paramod,[status(thm)],[c_13,c_24]) ).
cnf(c_23,plain,
$false,
inference(copy,[status(thm)],[c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP182-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:35:02 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3704606 was started by sandbox2 on n005,
% 0.17/0.43 % Fri Sep 25 14:35:02 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.17/0.44
% 0.17/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.44
% 0.17/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.44 % Length of proof is 4.
% 0.17/0.44 % Level of proof is 1.
% 0.17/0.44 % Maximum clause weight is 7.000.
% 0.17/0.44 % Given clauses 0.
% 0.17/0.44
% 0.17/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------