%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP138-1 : 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 : n015.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 07:28:06 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 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 : 31 ( 4 sgn 11 !; 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(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(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(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(ax_glb1a_1,axiom,
least_upper_bound(a,c) = a,
file('theBenchmark.p',ax_glb1a_1) ).
cnf(c_22,plain,
least_upper_bound(a,c) = a,
inference(clausify,[status(thm)],[ax_glb1a_1]) ).
fof(ax_glb1a_2,axiom,
least_upper_bound(b,c) = b,
file('theBenchmark.p',ax_glb1a_2) ).
cnf(c_23,plain,
least_upper_bound(b,c) = b,
inference(clausify,[status(thm)],[ax_glb1a_2]) ).
fof(prove_ax_glb1a,axiom,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b),
file('theBenchmark.p',prove_ax_glb1a) ).
cnf(c_24,plain,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b),
inference(clausify,[status(thm)],[prove_ax_glb1a]) ).
cnf(c_25,plain,
least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b),
inference(paramod,[status(thm)],[c_5,c_24]) ).
cnf(c_38,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,greatest_lower_bound(B,C))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_41,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_356,plain,
greatest_lower_bound(c,a) = c,
inference(paramod,[status(thm)],[c_22,c_41]) ).
cnf(c_105,plain,
greatest_lower_bound(a,c) = c,
inference(paramod,[status(thm)],[c_4,c_356]) ).
cnf(c_357,plain,
greatest_lower_bound(c,b) = c,
inference(paramod,[status(thm)],[c_23,c_41]) ).
cnf(c_106,plain,
greatest_lower_bound(b,c) = c,
inference(paramod,[status(thm)],[c_4,c_357]) ).
cnf(c_250,plain,
least_upper_bound(greatest_lower_bound(A,a),greatest_lower_bound(A,c)) = greatest_lower_bound(A,a),
inference(paramod,[status(thm)],[c_105,c_38]) ).
cnf(c_358,plain,
least_upper_bound(greatest_lower_bound(b,a),c) = greatest_lower_bound(b,a),
inference(paramod,[status(thm)],[c_106,c_250]) ).
cnf(c_359,plain,
least_upper_bound(greatest_lower_bound(a,b),c) = greatest_lower_bound(b,a),
inference(paramod,[status(thm)],[c_4,c_358]) ).
cnf(c_360,plain,
least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(b,a),
inference(paramod,[status(thm)],[c_5,c_359]) ).
cnf(c_354,plain,
least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
inference(paramod,[status(thm)],[c_4,c_360]) ).
cnf(c_355,plain,
$false,
inference(resolve,[status(thm)],[c_354,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP138-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 14:34:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1593047 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 14:34:27 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.44
% 0.09/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.44 % Length of proof is 17.
% 0.09/0.44 % Level of proof is 5.
% 0.09/0.44 % Maximum clause weight is 38.000.
% 0.09/0.44 % Given clauses 45.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------