%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP143-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 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(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(idempotence_of_gld,axiom,
! [VAR_0] : greatest_lower_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_gld) ).
cnf(c_11,plain,
greatest_lower_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_gld]) ).
fof(prove_ax_glb2b,axiom,
greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b),
file('theBenchmark.p',prove_ax_glb2b) ).
cnf(c_22,plain,
greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b),
inference(clausify,[status(thm)],[prove_ax_glb2b]) ).
cnf(c_23,plain,
greatest_lower_bound(a,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b),
inference(paramod,[status(thm)],[c_4,c_22]) ).
cnf(c_34,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_32,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_33,plain,
$false,
inference(resolve,[status(thm)],[c_32,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP143-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 14:37:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3531786 was started by sandbox on n001,
% 0.08/0.35 % Fri Sep 25 14:37:10 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 8.
% 0.08/0.37 % Level of proof is 3.
% 0.08/0.37 % Maximum clause weight is 11.000.
% 0.08/0.37 % Given clauses 9.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------