%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT091+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:03:06 AM UTC 2026
% Result : Theorem 0.17s 0.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 53 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 13 |; 3 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 47 ( 0 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',leq_def) ).
fof(less_implies_leq,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ),
file('theBenchmark.p',less_implies_leq) ).
fof(axis_compatible_def,axiom,
! [I1lo,I1hi,I2lo,I2hi] :
( axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ? [X] :
( in_closed(X,I2lo,I2hi)
& in_closed(X,I1lo,I1hi) ) ),
file('theBenchmark.p',axis_compatible_def) ).
fof(box2_overlap,axiom,
! [A1,B1,A2,B2,C1,D1,C2,D2] :
( box2_compatible(A1,B1,A2,B2,C1,D1,C2,D2)
<=> ( axis_compatible(A2,B2,C2,D2)
& axis_compatible(A1,B1,C1,D1) ) ),
file('theBenchmark.p',box2_overlap) ).
fof(shape_closed,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(X,B)
& leq(A,X) ) ),
file('theBenchmark.p',shape_closed) ).
fof(odrl624,conjecture,
box2_compatible(v0,v600,v0,v600,v400,v800,v400,v800),
file('theBenchmark.p',odrl624) ).
fof(odrl624_neg,negated_conjecture,
~ box2_compatible(v0,v600,v0,v600,v400,v800,v400,v800),
inference(assume_negation,[status(cth)],[odrl624]) ).
cnf(c_67,negated_conjecture,
~ box2_compatible(v0,v600,v0,v600,v400,v800,v400,v800),
inference(clausify,[status(thm)],[odrl624_neg]) ).
fof(ord_v400_v800,axiom,
less(v400,v800),
file('theBenchmark.p',ord_v400_v800) ).
cnf(c_77,plain,
less(v400,v800),
inference(clausify,[status(thm)],[ord_v400_v800]) ).
fof(ord_v400_v600,axiom,
less(v400,v600),
file('theBenchmark.p',ord_v400_v600) ).
cnf(c_78,plain,
less(v400,v600),
inference(clausify,[status(thm)],[ord_v400_v600]) ).
fof(ord_v0_v400,axiom,
less(v0,v400),
file('theBenchmark.p',ord_v0_v400) ).
cnf(c_80,plain,
less(v0,v400),
inference(clausify,[status(thm)],[ord_v0_v400]) ).
cnf(c_81,plain,
( ~ leq(A,C)
| ~ leq(B,A)
| in_closed(A,B,C) ),
inference(clausify,[status(thm)],[shape_closed]) ).
cnf(c_86,plain,
( ~ axis_compatible(C,D,V6,V7)
| ~ axis_compatible(A,B,E,F)
| box2_compatible(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[box2_overlap]) ).
cnf(c_110,plain,
( ~ in_closed(E,C,D)
| ~ in_closed(E,A,B)
| axis_compatible(A,B,C,D) ),
inference(clausify,[status(thm)],[axis_compatible_def]) ).
cnf(c_116,plain,
( leq(A,B)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_implies_leq]) ).
cnf(c_118,plain,
( B != A
| leq(A,B) ),
inference(clausify,[status(thm)],[leq_def]) ).
cnf(c_128,plain,
( ~ axis_compatible(A,B,C,D)
| box2_compatible(A,B,A,B,C,D,C,D) ),
inference(factor,[status(thm)],[c_86]) ).
cnf(c_180,plain,
leq(v0,v400),
inference(resolve,[status(thm)],[c_116,c_80]) ).
cnf(c_182,plain,
leq(v400,v600),
inference(resolve,[status(thm)],[c_116,c_78]) ).
cnf(c_183,plain,
leq(v400,v800),
inference(resolve,[status(thm)],[c_116,c_77]) ).
cnf(c_185,plain,
leq(A,A),
inference(xxres,[status(thm)],[c_118]) ).
cnf(c_216,negated_conjecture,
~ axis_compatible(v0,v600,v400,v800),
inference(resolve,[status(thm)],[c_128,c_67]) ).
cnf(c_238,plain,
( ~ leq(v400,A)
| in_closed(v400,v0,A) ),
inference(resolve,[status(thm)],[c_180,c_81]) ).
cnf(c_366,plain,
in_closed(v400,v0,v600),
inference(resolve,[status(thm)],[c_238,c_182]) ).
cnf(c_407,plain,
( ~ in_closed(A,v400,v800)
| ~ in_closed(A,v0,v600) ),
inference(resolve,[status(thm)],[c_110,c_216]) ).
cnf(c_402,plain,
~ in_closed(v400,v400,v800),
inference(resolve,[status(thm)],[c_407,c_366]) ).
cnf(c_408,plain,
( ~ leq(v400,v800)
| ~ leq(v400,v400) ),
inference(resolve,[status(thm)],[c_81,c_402]) ).
cnf(c_409,plain,
~ leq(v400,v400),
inference(resolve,[status(thm)],[c_408,c_183]) ).
cnf(c_406,plain,
$false,
inference(resolve,[status(thm)],[c_185,c_409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT091+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 00:10:24 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2251187 was started by sandbox2 on n007,
% 0.17/0.43 % Sat Sep 26 00:10:24 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.53
% 0.17/0.53 % SZS status Theorem for theBenchmark
% 0.17/0.53
% 0.17/0.53 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.17/0.53 % Length of proof is 25.
% 0.17/0.53 % Level of proof is 6.
% 0.17/0.53 % Maximum clause weight is 24.000.
% 0.17/0.53 % Given clauses 169.
% 0.17/0.53
% 0.17/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------