%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT080+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 : n006.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 : 28 ( 13 unt; 0 def)
% Number of atoms : 104 ( 43 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 125 ( 49 ~; 8 |; 65 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 29 ( 2 sgn 7 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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_closed,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(X,B)
& leq(A,X) ) ),
file('theBenchmark.p',in_closed) ).
fof(distinct,axiom,
( v600 != v800
& v500 != v800
& v500 != v600
& v300 != v800
& v300 != v600
& v300 != v500
& v150 != v800
& v150 != v600
& v150 != v500
& v150 != v300
& v100 != v800
& v100 != v600
& v100 != v500
& v100 != v300
& v100 != v150
& v32 != v800
& v32 != v600
& v32 != v500
& v32 != v300
& v32 != v150
& v32 != v100
& v8 != v800
& v8 != v600
& v8 != v500
& v8 != v300
& v8 != v150
& v8 != v100
& v8 != v32
& v0 != v800
& v0 != v600
& v0 != v500
& v0 != v300
& v0 != v150
& v0 != v100
& v0 != v32
& v0 != v8 ),
file('theBenchmark.p',distinct) ).
fof(odrl365,conjecture,
~ ? [X,Y,Z,W] :
( leq(v150,W)
& in_lopen(W,v0,v300)
& in_lopen(Z,v0,v32)
& leq(v8,Z)
& in_open(Y,v0,v500)
& less(v100,Y)
& in_closed(X,v800,v800)
& in_closed(X,v600,v600) ),
file('theBenchmark.p',odrl365) ).
fof(odrl365_neg,negated_conjecture,
~ ~ ? [X,Y,Z,W] :
( leq(v150,W)
& in_lopen(W,v0,v300)
& in_lopen(Z,v0,v32)
& leq(v8,Z)
& in_open(Y,v0,v500)
& less(v100,Y)
& in_closed(X,v800,v800)
& in_closed(X,v600,v600) ),
inference(assume_negation,[status(cth)],[odrl365]) ).
fof(nnf_23,plain,
? [X,Y,Z,W] :
( leq(v150,W)
& in_lopen(W,v0,v300)
& in_lopen(Z,v0,v32)
& leq(v8,Z)
& in_open(Y,v0,v500)
& less(v100,Y)
& in_closed(X,v800,v800)
& in_closed(X,v600,v600) ),
inference(fof_nnf,[status(thm)],[odrl365_neg]) ).
fof(sk_odrl365_neg,plain,
( leq(v150,sK3)
& in_lopen(sK3,v0,v300)
& in_lopen(sK2,v0,v32)
& leq(v8,sK2)
& in_open(sK1,v0,v500)
& less(v100,sK1)
& in_closed(sK0,v800,v800)
& in_closed(sK0,v600,v600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2),skolemize(W,sK3)],[nnf_23]) ).
cnf(c_56,negated_conjecture,
in_closed(sK0,v800,v800),
inference(split_conjunct,[status(thm)],[sk_odrl365_neg]) ).
cnf(c_57,negated_conjecture,
in_closed(sK0,v600,v600),
inference(split_conjunct,[status(thm)],[sk_odrl365_neg]) ).
cnf(c_58,plain,
v800 != v600,
inference(clausify,[status(thm)],[distinct]) ).
fof(ord_v600_v800,axiom,
less(v600,v800),
file('theBenchmark.p',ord_v600_v800) ).
cnf(c_114,plain,
less(v600,v800),
inference(clausify,[status(thm)],[ord_v600_v800]) ).
cnf(c_172,plain,
( leq(A,C)
| ~ in_closed(A,B,C) ),
inference(clausify,[status(thm)],[in_closed]) ).
cnf(c_173,plain,
( leq(B,A)
| ~ in_closed(A,B,C) ),
inference(clausify,[status(thm)],[in_closed]) ).
cnf(c_177,plain,
( leq(A,B)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_implies_leq]) ).
cnf(c_178,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_antisym]) ).
cnf(c_229,plain,
leq(sK0,v600),
inference(resolve,[status(thm)],[c_172,c_57]) ).
cnf(c_231,plain,
leq(v600,sK0),
inference(resolve,[status(thm)],[c_173,c_57]) ).
cnf(c_232,plain,
leq(v800,sK0),
inference(resolve,[status(thm)],[c_173,c_56]) ).
cnf(c_284,plain,
leq(v600,v800),
inference(resolve,[status(thm)],[c_177,c_114]) ).
cnf(c_661,plain,
( sK0 = v600
| ~ leq(v600,sK0) ),
inference(resolve,[status(thm)],[c_229,c_178]) ).
cnf(c_418,plain,
sK0 = v600,
inference(resolve,[status(thm)],[c_231,c_661]) ).
cnf(c_662,plain,
( v600 = v800
| ~ leq(v800,v600) ),
inference(resolve,[status(thm)],[c_284,c_178]) ).
cnf(c_663,plain,
( v800 = v600
| ~ leq(v800,v600) ),
inference(copy,[status(thm)],[c_662]) ).
cnf(c_627,plain,
~ leq(v800,v600),
inference(resolve,[status(thm)],[c_58,c_663]) ).
cnf(c_664,plain,
leq(v800,v600),
inference(paramod,[status(thm)],[c_418,c_232]) ).
cnf(c_660,plain,
$false,
inference(resolve,[status(thm)],[c_627,c_664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT080+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n006.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
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 00:12:19 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 4100004 was started by sandbox2 on n006,
% 0.09/5.38 % Sat Sep 26 00:12:19 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % 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 20.
% 0.15/5.43 % Level of proof is 4.
% 0.15/5.43 % Maximum clause weight is 14.000.
% 0.15/5.43 % Given clauses 218.
% 0.15/5.43
% 0.15/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------