%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:03:07 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 7 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(leq_less_trans,axiom,
! [X,Y,Z] :
( ( less(Y,Z)
& leq(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',leq_less_trans) ).
fof(leq_trans,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('theBenchmark.p',leq_trans) ).
fof(in_lopen,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( leq(X,B)
& less(A,X) ) ),
file('theBenchmark.p',in_lopen) ).
cnf(c_24,plain,
( leq(A,C)
| ~ in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
fof(wit_in_lopen,axiom,
in_lopen(w,v0,v600),
file('theBenchmark.p',wit_in_lopen) ).
cnf(c_26,plain,
in_lopen(w,v0,v600),
inference(clausify,[status(thm)],[wit_in_lopen]) ).
cnf(c_45,plain,
leq(w,v600),
inference(resolve,[status(thm)],[c_26,c_24]) ).
fof(wit_leq,axiom,
leq(v800,w),
file('theBenchmark.p',wit_leq) ).
cnf(c_46,plain,
leq(v800,w),
inference(clausify,[status(thm)],[wit_leq]) ).
fof(ord_v600_v800,axiom,
less(v600,v800),
file('theBenchmark.p',ord_v600_v800) ).
cnf(c_51,plain,
less(v600,v800),
inference(clausify,[status(thm)],[ord_v600_v800]) ).
cnf(c_77,plain,
( leq(A,C)
| ~ leq(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_trans]) ).
cnf(c_79,plain,
( less(A,C)
| ~ less(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_less_trans]) ).
cnf(c_86,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_195,plain,
( less(A,v800)
| ~ leq(A,v600) ),
inference(resolve,[status(thm)],[c_79,c_51]) ).
cnf(c_159,plain,
~ leq(v800,v600),
inference(resolve,[status(thm)],[c_195,c_86]) ).
cnf(c_196,plain,
( leq(A,v600)
| ~ leq(A,w) ),
inference(resolve,[status(thm)],[c_77,c_45]) ).
cnf(c_197,plain,
~ leq(v800,w),
inference(resolve,[status(thm)],[c_196,c_159]) ).
cnf(c_194,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n019.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 00:14:05 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 4058819 was started by sandbox on n019,
% 0.19/0.45 % Sat Sep 26 00:14:05 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.50
% 0.19/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.50
% 0.19/0.50 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.50 % Length of proof is 14.
% 0.19/0.50 % Level of proof is 3.
% 0.19/0.50 % Maximum clause weight is 14.000.
% 0.19/0.50 % Given clauses 58.
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------