%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT082+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 : n001.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 0.15s 5.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 60 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 14 ~; 8 |; 23 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 31 ( 2 sgn 9 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(leq_antisym,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
=> X = Y ),
file('theBenchmark.p',leq_antisym) ).
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_closed,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(X,B)
& leq(A,X) ) ),
file('theBenchmark.p',in_closed) ).
fof(odrl411,conjecture,
~ ? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
file('theBenchmark.p',odrl411) ).
fof(odrl411_neg,negated_conjecture,
~ ~ ? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
inference(assume_negation,[status(cth)],[odrl411]) ).
fof(nnf_23,plain,
? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
inference(fof_nnf,[status(thm)],[odrl411_neg]) ).
fof(sk_odrl411_neg,plain,
( in_lopen(sK2,v0,v32)
& leq(v16,sK2)
& in_open(sK1,v0,v500)
& less(v300,sK1)
& in_closed(sK0,v601,v601)
& in_closed(sK0,v600,v600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_23]) ).
cnf(c_52,negated_conjecture,
in_closed(sK0,v601,v601),
inference(split_conjunct,[status(thm)],[sk_odrl411_neg]) ).
cnf(c_53,negated_conjecture,
in_closed(sK0,v600,v600),
inference(split_conjunct,[status(thm)],[sk_odrl411_neg]) ).
fof(ord_v600_v601,axiom,
less(v600,v601),
file('theBenchmark.p',ord_v600_v601) ).
cnf(c_84,plain,
less(v600,v601),
inference(clausify,[status(thm)],[ord_v600_v601]) ).
cnf(c_127,plain,
( leq(A,C)
| ~ in_closed(A,B,C) ),
inference(clausify,[status(thm)],[in_closed]) ).
cnf(c_128,plain,
( leq(B,A)
| ~ in_closed(A,B,C) ),
inference(clausify,[status(thm)],[in_closed]) ).
cnf(c_131,plain,
( less(A,C)
| ~ less(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_less_trans]) ).
cnf(c_133,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_antisym]) ).
cnf(c_138,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_180,plain,
leq(sK0,v600),
inference(resolve,[status(thm)],[c_127,c_53]) ).
cnf(c_182,plain,
leq(v600,sK0),
inference(resolve,[status(thm)],[c_128,c_53]) ).
cnf(c_183,plain,
leq(v601,sK0),
inference(resolve,[status(thm)],[c_128,c_52]) ).
cnf(c_371,plain,
( less(A,v601)
| ~ leq(A,v600) ),
inference(resolve,[status(thm)],[c_131,c_84]) ).
cnf(c_324,plain,
~ leq(v601,v600),
inference(resolve,[status(thm)],[c_371,c_138]) ).
cnf(c_372,plain,
( sK0 = v600
| ~ leq(v600,sK0) ),
inference(resolve,[status(thm)],[c_180,c_133]) ).
cnf(c_355,plain,
sK0 = v600,
inference(resolve,[status(thm)],[c_182,c_372]) ).
cnf(c_373,plain,
leq(v601,v600),
inference(paramod,[status(thm)],[c_355,c_183]) ).
cnf(c_370,plain,
$false,
inference(resolve,[status(thm)],[c_324,c_373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n001.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 00:18:03 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 405557 was started by sandbox on n001,
% 0.11/5.39 % Sat Sep 26 00:18:03 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.40
% 0.11/5.40 % From the command line: assign(max_seconds, 300).
% 0.15/5.43
% 0.15/5.43 % SZS status Theorem for theBenchmark
% 0.15/5.43
% 0.15/5.43 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/5.43 % Length of proof is 19.
% 0.15/5.43 % Level of proof is 4.
% 0.15/5.43 % Maximum clause weight is 9.000.
% 0.15/5.43 % Given clauses 94.
% 0.15/5.43
% 0.15/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------