%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT075+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 : n018.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 08:03:04 AM UTC 2026
% Result : Theorem 0.11s 0.48s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 34 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 10 ~; 5 |; 6 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 19 ( 1 sgn 8 !; 3 ?)
% 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(less_implies_leq,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ),
file('theBenchmark.p',less_implies_leq) ).
fof(in_open,axiom,
! [X,A,B] :
( in_open(X,A,B)
<=> ( less(X,B)
& less(A,X) ) ),
file('theBenchmark.p',in_open) ).
fof(odrl302,conjecture,
~ ? [X] :
( leq(v600,X)
& in_open(X,v0,v600) ),
file('theBenchmark.p',odrl302) ).
fof(odrl302_neg,negated_conjecture,
~ ~ ? [X] :
( leq(v600,X)
& in_open(X,v0,v600) ),
inference(assume_negation,[status(cth)],[odrl302]) ).
cnf(c_30,plain,
( less(A,C)
| ~ in_open(A,B,C) ),
inference(clausify,[status(thm)],[in_open]) ).
fof(nnf_22,plain,
? [X] :
( leq(v600,X)
& in_open(X,v0,v600) ),
inference(fof_nnf,[status(thm)],[odrl302_neg]) ).
fof(sk_odrl302_neg,plain,
( leq(v600,sK0)
& in_open(sK0,v0,v600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_22]) ).
cnf(c_32,negated_conjecture,
in_open(sK0,v0,v600),
inference(split_conjunct,[status(thm)],[sk_odrl302_neg]) ).
cnf(c_45,negated_conjecture,
less(sK0,v600),
inference(resolve,[status(thm)],[c_32,c_30]) ).
cnf(c_46,negated_conjecture,
leq(v600,sK0),
inference(split_conjunct,[status(thm)],[sk_odrl302_neg]) ).
cnf(c_76,plain,
( leq(A,B)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_implies_leq]) ).
cnf(c_77,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_antisym]) ).
cnf(c_82,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_123,plain,
leq(sK0,v600),
inference(resolve,[status(thm)],[c_76,c_45]) ).
cnf(c_132,negated_conjecture,
( sK0 = v600
| ~ leq(sK0,v600) ),
inference(resolve,[status(thm)],[c_77,c_46]) ).
cnf(c_125,negated_conjecture,
sK0 = v600,
inference(resolve,[status(thm)],[c_123,c_132]) ).
cnf(c_133,negated_conjecture,
less(v600,v600),
inference(paramod,[status(thm)],[c_125,c_45]) ).
cnf(c_131,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_82,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42 % Computer : n018.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sat Sep 26 00:14:05 UTC 2026
% 0.11/0.43 % CPUTime :
% 0.11/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.43 % Process 3187944 was started by sandbox on n018,
% 0.11/0.43 % Sat Sep 26 00:14:05 2026
% 0.11/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.44
% 0.11/0.44 % From the command line: assign(max_seconds, 300).
% 0.11/0.48
% 0.11/0.48 % SZS status Theorem for theBenchmark
% 0.11/0.48
% 0.11/0.48 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.11/0.48 % Length of proof is 15.
% 0.11/0.48 % Level of proof is 5.
% 0.11/0.48 % Maximum clause weight is 9.000.
% 0.11/0.48 % Given clauses 28.
% 0.11/0.48
% 0.11/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------