%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM025-2 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 08:16:04 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_less,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ greater_or_equalish(VAR_2,VAR_1)
| greater_or_equalish(VAR_2,VAR_0)
| greater_or_equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less) ).
cnf(c_10,plain,
( ~ greater_or_equalish(C,B)
| greater_or_equalish(C,A)
| greater_or_equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less]) ).
fof(no_number_less_than_itself,axiom,
! [VAR_0] : greater_or_equalish(VAR_0,VAR_0),
file('theBenchmark.p',no_number_less_than_itself) ).
cnf(c_14,plain,
greater_or_equalish(A,A),
inference(clausify,[status(thm)],[no_number_less_than_itself]) ).
fof(a_less_than_b,axiom,
~ greater_or_equalish(a,b),
file('theBenchmark.p',a_less_than_b) ).
cnf(c_15,plain,
~ greater_or_equalish(a,b),
inference(clausify,[status(thm)],[a_less_than_b]) ).
fof(prove_b_not_less_than_a,axiom,
~ greater_or_equalish(b,a),
file('theBenchmark.p',prove_b_not_less_than_a) ).
cnf(c_16,plain,
~ greater_or_equalish(b,a),
inference(clausify,[status(thm)],[prove_b_not_less_than_a]) ).
cnf(c_47,plain,
( ~ greater_or_equalish(A,b)
| greater_or_equalish(A,a) ),
inference(resolve,[status(thm)],[c_10,c_15]) ).
cnf(c_48,plain,
~ greater_or_equalish(b,b),
inference(resolve,[status(thm)],[c_47,c_16]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM025-2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 01:54:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3111814 was started by sandbox on n009,
% 0.09/0.35 % Sat Sep 26 01:54:14 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.09/0.36
% 0.09/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.36
% 0.09/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.36 % Length of proof is 5.
% 0.09/0.36 % Level of proof is 1.
% 0.09/0.36 % Maximum clause weight is 9.000.
% 0.09/0.36 % Given clauses 16.
% 0.09/0.36
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------