%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM025-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:16:03 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% 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 ( 2 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] :
( less(VAR_2,VAR_1)
| ~ less(VAR_2,VAR_0)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less) ).
cnf(c_7,plain,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less]) ).
fof(no_number_less_than_itself,axiom,
! [VAR_0] : ~ less(VAR_0,VAR_0),
file('theBenchmark.p',no_number_less_than_itself) ).
cnf(c_14,plain,
~ less(A,A),
inference(clausify,[status(thm)],[no_number_less_than_itself]) ).
fof(a_less_than_b,axiom,
less(a,b),
file('theBenchmark.p',a_less_than_b) ).
cnf(c_15,plain,
less(a,b),
inference(clausify,[status(thm)],[a_less_than_b]) ).
fof(prove_b_not_less_than_a,axiom,
less(b,a),
file('theBenchmark.p',prove_b_not_less_than_a) ).
cnf(c_16,plain,
less(b,a),
inference(clausify,[status(thm)],[prove_b_not_less_than_a]) ).
cnf(c_44,plain,
( less(a,A)
| ~ less(b,A) ),
inference(resolve,[status(thm)],[c_7,c_15]) ).
cnf(c_42,plain,
~ less(b,a),
inference(resolve,[status(thm)],[c_44,c_14]) ).
cnf(c_43,plain,
$false,
inference(resolve,[status(thm)],[c_42,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM025-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 01:56:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4028360 was started by sandbox2 on n026,
% 0.10/0.37 % Sat Sep 26 01:56:55 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 6.
% 0.10/0.38 % Level of proof is 2.
% 0.10/0.38 % Maximum clause weight is 9.000.
% 0.10/0.38 % Given clauses 15.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------