%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT084+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 : n006.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 08:03:05 AM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 38 ( 10 ~; 4 |; 22 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 24 ( 1 sgn 7 !; 9 ?)
% 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(in_lopen,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( leq(X,B)
& less(A,X) ) ),
file('theBenchmark.p',in_lopen) ).
fof(odrl432,conjecture,
~ ? [X,Y,Z] :
( leq(v200,Z)
& in_lopen(Z,v0,v200)
& less(v400,Y)
& in_lopen(Y,v0,v400)
& leq(v600,X)
& in_lopen(X,v0,v600) ),
file('theBenchmark.p',odrl432) ).
fof(odrl432_neg,negated_conjecture,
~ ~ ? [X,Y,Z] :
( leq(v200,Z)
& in_lopen(Z,v0,v200)
& less(v400,Y)
& in_lopen(Y,v0,v400)
& leq(v600,X)
& in_lopen(X,v0,v600) ),
inference(assume_negation,[status(cth)],[odrl432]) ).
cnf(c_25,plain,
( leq(A,C)
| ~ in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
fof(nnf_23,plain,
? [X,Y,Z] :
( leq(v200,Z)
& in_lopen(Z,v0,v200)
& less(v400,Y)
& in_lopen(Y,v0,v400)
& leq(v600,X)
& in_lopen(X,v0,v600) ),
inference(fof_nnf,[status(thm)],[odrl432_neg]) ).
fof(sk_odrl432_neg,plain,
( leq(v200,sK2)
& in_lopen(sK2,v0,v200)
& less(v400,sK0)
& in_lopen(sK0,v0,v400)
& leq(v600,sK1)
& in_lopen(sK1,v0,v600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(X,sK1),skolemize(Y,sK0),skolemize(Z,sK2)],[nnf_23]) ).
cnf(c_28,negated_conjecture,
in_lopen(sK0,v0,v400),
inference(split_conjunct,[status(thm)],[sk_odrl432_neg]) ).
cnf(c_50,negated_conjecture,
leq(sK0,v400),
inference(resolve,[status(thm)],[c_28,c_25]) ).
cnf(c_54,negated_conjecture,
less(v400,sK0),
inference(split_conjunct,[status(thm)],[sk_odrl432_neg]) ).
cnf(c_94,plain,
( less(A,C)
| ~ less(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_less_trans]) ).
cnf(c_101,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_223,negated_conjecture,
( less(A,sK0)
| ~ leq(A,v400) ),
inference(resolve,[status(thm)],[c_94,c_54]) ).
cnf(c_224,negated_conjecture,
~ leq(sK0,v400),
inference(resolve,[status(thm)],[c_223,c_101]) ).
cnf(c_222,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_50,c_224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT084+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n006.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 00:12:45 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 4101461 was started by sandbox on n006,
% 0.10/5.38 % Sat Sep 26 00:12:45 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Theorem for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 11.
% 0.14/5.40 % Level of proof is 3.
% 0.14/5.40 % Maximum clause weight is 14.000.
% 0.14/5.40 % Given clauses 49.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------