%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT079+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 : n016.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 4.35s 21.04s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 87 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 33 ~; 33 |; 12 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 54 ( 13 sgn 11 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(trichotomy,axiom,
! [X,Y] :
( less(Y,X)
| X = Y
| less(X,Y) ),
file('theBenchmark.p',trichotomy) ).
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',leq_def) ).
fof(less_leq_trans,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& less(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',less_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) ).
fof(odrl350,conjecture,
? [X,Y,Z] :
( ~ ( in_lopen(Z,v0,v16)
& in_lopen(Y,v0,v800)
& in_lopen(X,v0,v1200) )
& in_lopen(Z,v0,v32)
& in_lopen(Y,v0,v400)
& in_lopen(X,v0,v600) ),
file('theBenchmark.p',odrl350) ).
fof(odrl350_neg,negated_conjecture,
~ ? [X,Y,Z] :
( ~ ( in_lopen(Z,v0,v16)
& in_lopen(Y,v0,v800)
& in_lopen(X,v0,v1200) )
& in_lopen(Z,v0,v32)
& in_lopen(Y,v0,v400)
& in_lopen(X,v0,v600) ),
inference(assume_negation,[status(cth)],[odrl350]) ).
cnf(c_41,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_43,plain,
( less(B,A)
| B = A
| less(A,B) ),
inference(clausify,[status(thm)],[trichotomy]) ).
cnf(c_46,plain,
( B != A
| leq(A,B) ),
inference(clausify,[status(thm)],[leq_def]) ).
cnf(c_49,plain,
( less(A,C)
| ~ leq(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_leq_trans]) ).
cnf(c_55,plain,
( leq(A,C)
| ~ in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
cnf(c_56,plain,
( ~ leq(A,C)
| ~ less(B,A)
| in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
fof(ord_v0_v32,axiom,
less(v0,v32),
file('theBenchmark.p',ord_v0_v32) ).
cnf(c_79,plain,
less(v0,v32),
inference(clausify,[status(thm)],[ord_v0_v32]) ).
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]) ).
fof(ord_v0_v600,axiom,
less(v0,v600),
file('theBenchmark.p',ord_v0_v600) ).
cnf(c_81,plain,
less(v0,v600),
inference(clausify,[status(thm)],[ord_v0_v600]) ).
fof(ord_v16_v32,axiom,
less(v16,v32),
file('theBenchmark.p',ord_v16_v32) ).
cnf(c_84,plain,
less(v16,v32),
inference(clausify,[status(thm)],[ord_v16_v32]) ).
cnf(c_127,negated_conjecture,
( in_lopen(C,v0,v16)
| ~ in_lopen(C,v0,v32)
| ~ in_lopen(B,v0,v400)
| ~ in_lopen(A,v0,v600) ),
inference(clausify,[status(thm)],[odrl350_neg]) ).
cnf(c_146,plain,
leq(A,A),
inference(xxres,[status(thm)],[c_46]) ).
cnf(c_213,plain,
( ~ leq(v32,A)
| in_lopen(v32,v0,A) ),
inference(resolve,[status(thm)],[c_79,c_56]) ).
cnf(c_223,plain,
( ~ leq(v400,A)
| in_lopen(v400,v0,A) ),
inference(resolve,[status(thm)],[c_80,c_56]) ).
cnf(c_233,plain,
( ~ leq(v600,A)
| in_lopen(v600,v0,A) ),
inference(resolve,[status(thm)],[c_81,c_56]) ).
cnf(c_4329,plain,
( less(v16,A)
| ~ leq(v32,A) ),
inference(resolve,[status(thm)],[c_49,c_84]) ).
cnf(c_269,plain,
~ leq(v32,v16),
inference(resolve,[status(thm)],[c_4329,c_41]) ).
cnf(c_469,plain,
( in_lopen(D,v0,v16)
| ~ in_lopen(D,v0,v32)
| ~ in_lopen(C,A,v400)
| ~ in_lopen(B,v0,v600)
| less(v0,A)
| less(A,v0) ),
inference(paramod,[status(thm)],[c_43,c_127]) ).
cnf(c_652,plain,
~ in_lopen(v32,A,v16),
inference(resolve,[status(thm)],[c_55,c_269]) ).
cnf(c_1607,plain,
in_lopen(v32,v0,v32),
inference(resolve,[status(thm)],[c_213,c_146]) ).
cnf(c_1672,plain,
in_lopen(v400,v0,v400),
inference(resolve,[status(thm)],[c_223,c_146]) ).
cnf(c_1735,plain,
in_lopen(v600,v0,v600),
inference(resolve,[status(thm)],[c_233,c_146]) ).
cnf(c_4330,plain,
( in_lopen(C,v0,v16)
| ~ in_lopen(C,v0,v32)
| ~ in_lopen(B,v0,v400)
| ~ in_lopen(A,v0,v600)
| less(v0,v0) ),
inference(resolve,[status(thm)],[c_469,c_41]) ).
cnf(c_4331,plain,
( in_lopen(C,v0,v16)
| ~ in_lopen(C,v0,v32)
| ~ in_lopen(B,v0,v400)
| ~ in_lopen(A,v0,v600) ),
inference(resolve,[status(thm)],[c_4330,c_41]) ).
cnf(c_4332,plain,
( in_lopen(B,v0,v16)
| ~ in_lopen(B,v0,v32)
| ~ in_lopen(A,v0,v600) ),
inference(resolve,[status(thm)],[c_4331,c_1672]) ).
cnf(c_4333,plain,
( in_lopen(v32,v0,v16)
| ~ in_lopen(A,v0,v600) ),
inference(resolve,[status(thm)],[c_4332,c_1607]) ).
cnf(c_4327,plain,
~ in_lopen(A,v0,v600),
inference(resolve,[status(thm)],[c_4333,c_652]) ).
cnf(c_4328,plain,
$false,
inference(resolve,[status(thm)],[c_4327,c_1735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT079+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.03/20.49 % CPULimit : 300
% 0.03/20.49 % WCLimit : 300
% 0.03/20.49 % DateTime : Sat Sep 26 00:12:19 UTC 2026
% 0.03/20.49 % CPUTime :
% 0.03/20.49 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/20.49 % Process 3408400 was started by sandbox on n012,
% 0.03/20.49 % Sat Sep 26 00:12:19 2026
% 0.03/20.49 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/20.49
% 0.03/20.49 % From the command line: assign(max_seconds, 300).
% 4.35/21.04
% 4.35/21.04 % given #500 (T,wt=6): 2210 in_lopen(v1200,v16,v1200). [resolve(303,b,146,a)].
% 4.35/21.04
% 4.35/21.04 % SZS status Theorem for theBenchmark
% 4.35/21.04
% 4.35/21.04 % Proof 1 at 0.36 (+ 0.19) seconds.
% 4.35/21.04 % Length of proof is 29.
% 4.35/21.04 % Level of proof is 5.
% 4.35/21.04 % Maximum clause weight is 24.000.
% 4.35/21.04 % Given clauses 728.
% 4.35/21.04
% 4.35/21.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------