%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP144-1 : 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 : 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 07:28:07 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.35s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 14 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
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(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(prove_ax_glb3a,axiom,
least_upper_bound(greatest_lower_bound(a,b),b) != b,
file('theBenchmark.p',prove_ax_glb3a) ).
cnf(c_22,plain,
least_upper_bound(greatest_lower_bound(a,b),b) != b,
inference(clausify,[status(thm)],[prove_ax_glb3a]) ).
cnf(c_23,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) != b,
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_35,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_36,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP144-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n007.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 25 14:29:38 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.34 % Process 1209768 was started by sandbox2 on n007,
% 0.06/0.34 % Fri Sep 25 14:29:38 2026
% 0.06/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.34
% 0.06/0.34 % From the command line: assign(max_seconds, 300).
% 0.06/0.35
% 0.06/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.06/0.35
% 0.06/0.35 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.06/0.35 % Length of proof is 7.
% 0.06/0.35 % Level of proof is 2.
% 0.06/0.35 % Maximum clause weight is 7.000.
% 0.06/0.35 % Given clauses 10.
% 0.06/0.35
% 0.06/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------