%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT078+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 : 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 0.16s 5.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 96 ( 32 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 15 |; 43 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 35 ( 1 sgn 12 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(transitive,axiom,
! [X,Y,Z] :
( ( less(Y,Z)
& less(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',transitive) ).
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',leq_def) ).
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(distinct,axiom,
( v800 != v1200
& v600 != v1200
& v600 != v800
& v200 != v1200
& v200 != v800
& v200 != v600
& v32 != v1200
& v32 != v800
& v32 != v600
& v32 != v200
& v8 != v1200
& v8 != v800
& v8 != v600
& v8 != v200
& v8 != v32
& v0 != v1200
& v0 != v800
& v0 != v600
& v0 != v200
& v0 != v32
& v0 != v8 ),
file('theBenchmark.p',distinct) ).
fof(odrl341,conjecture,
~ ? [X,Y,Z] :
( leq(v8,Z)
& in_lopen(Z,v0,v32)
& leq(v200,Y)
& in_lopen(Y,v0,v800)
& leq(v1200,X)
& in_lopen(X,v0,v600) ),
file('theBenchmark.p',odrl341) ).
fof(odrl341_neg,negated_conjecture,
~ ~ ? [X,Y,Z] :
( leq(v8,Z)
& in_lopen(Z,v0,v32)
& leq(v200,Y)
& in_lopen(Y,v0,v800)
& leq(v1200,X)
& in_lopen(X,v0,v600) ),
inference(assume_negation,[status(cth)],[odrl341]) ).
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(v8,Z)
& in_lopen(Z,v0,v32)
& leq(v200,Y)
& in_lopen(Y,v0,v800)
& leq(v1200,X)
& in_lopen(X,v0,v600) ),
inference(fof_nnf,[status(thm)],[odrl341_neg]) ).
fof(sk_odrl341_neg,plain,
( leq(v8,sK2)
& in_lopen(sK2,v0,v32)
& leq(v200,sK1)
& in_lopen(sK1,v0,v800)
& leq(v1200,sK0)
& in_lopen(sK0,v0,v600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_23]) ).
cnf(c_27,negated_conjecture,
in_lopen(sK0,v0,v600),
inference(split_conjunct,[status(thm)],[sk_odrl341_neg]) ).
cnf(c_52,negated_conjecture,
leq(sK0,v600),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_55,negated_conjecture,
leq(v1200,sK0),
inference(split_conjunct,[status(thm)],[sk_odrl341_neg]) ).
cnf(c_58,plain,
v1200 != v600,
inference(clausify,[status(thm)],[distinct]) ).
cnf(c_59,plain,
v600 != v1200,
inference(copy,[status(thm)],[c_58]) ).
fof(ord_v600_v1200,axiom,
less(v600,v1200),
file('theBenchmark.p',ord_v600_v1200) ).
cnf(c_87,plain,
less(v600,v1200),
inference(clausify,[status(thm)],[ord_v600_v1200]) ).
cnf(c_133,plain,
( less(A,C)
| ~ less(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_less_trans]) ).
cnf(c_137,plain,
( B = A
| less(A,B)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_def]) ).
cnf(c_139,plain,
( less(A,C)
| ~ less(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitive]) ).
cnf(c_140,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_284,plain,
( sK0 = v1200
| less(v1200,sK0) ),
inference(resolve,[status(thm)],[c_137,c_55]) ).
cnf(c_522,negated_conjecture,
( v600 = sK0
| less(sK0,v600) ),
inference(resolve,[status(thm)],[c_137,c_52]) ).
cnf(c_287,negated_conjecture,
( sK0 = v600
| less(sK0,v600) ),
inference(copy,[status(thm)],[c_522]) ).
cnf(c_523,plain,
( less(A,v1200)
| ~ less(A,v600) ),
inference(resolve,[status(thm)],[c_139,c_87]) ).
cnf(c_367,plain,
~ less(v1200,v600),
inference(resolve,[status(thm)],[c_523,c_140]) ).
cnf(c_524,negated_conjecture,
( less(v1200,A)
| ~ less(sK0,A) ),
inference(resolve,[status(thm)],[c_133,c_55]) ).
cnf(c_518,negated_conjecture,
~ less(sK0,v600),
inference(resolve,[status(thm)],[c_524,c_367]) ).
cnf(c_520,negated_conjecture,
sK0 = v600,
inference(resolve,[status(thm)],[c_518,c_287]) ).
cnf(c_525,plain,
( sK0 = v1200
| less(v1200,v600) ),
inference(paramod,[status(thm)],[c_520,c_284]) ).
cnf(c_526,plain,
( v600 = v1200
| less(v1200,v600) ),
inference(paramod,[status(thm)],[c_520,c_525]) ).
cnf(c_527,plain,
v600 = v1200,
inference(resolve,[status(thm)],[c_367,c_526]) ).
cnf(c_521,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT078+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n018.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 00:14:28 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.40 % Process 3189490 was started by sandbox2 on n018,
% 0.16/5.40 % Sat Sep 26 00:14:28 2026
% 0.16/5.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.42
% 0.16/5.42 % From the command line: assign(max_seconds, 300).
% 0.16/5.48
% 0.16/5.48 % SZS status Theorem for theBenchmark
% 0.16/5.48
% 0.16/5.48 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/5.48 % Length of proof is 24.
% 0.16/5.48 % Level of proof is 5.
% 0.16/5.48 % Maximum clause weight is 14.000.
% 0.16/5.48 % Given clauses 138.
% 0.16/5.48
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------