%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : Tue Sep 8 06:16:15 AM UTC 2026
% Result : Theorem 119.84s 120.17s
% Output : CNFRefutation 119.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 17 |; 7 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 39 ( 9 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(completion_compat,axiom,
! [V,InfD,SupD] :
( ( leq(InfD,V)
& leq(V,SupD) )
=> completion_compatible(V,InfD,SupD) ) ).
fof(h_inf_lb,hypothesis,
! [X] : leq(ninf,X) ).
fof(h_sup_ub,hypothesis,
! [X] : leq(X,nsup) ).
fof(unknown_sound_compatible,conjecture,
? [V] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ) ).
fof(subgoal_0,plain,
? [V] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(strip,[],[unknown_sound_compatible]) ).
fof(negate_0_0,plain,
~ ? [V] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : leq(X,nsup),
inference(canonicalize,[],[h_sup_ub]) ).
fof(normalize_0_1,plain,
! [X] : leq(X,nsup),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : leq(ninf,X),
inference(canonicalize,[],[h_inf_lb]) ).
fof(normalize_0_3,plain,
! [X] : leq(ninf,X),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [InfD,SupD,V] :
( ~ leq(InfD,V)
| ~ leq(V,SupD)
| completion_compatible(V,InfD,SupD) ),
inference(canonicalize,[],[completion_compat]) ).
fof(normalize_0_5,plain,
! [InfD,SupD,V] :
( ~ leq(InfD,V)
| ~ leq(V,SupD)
| completion_compatible(V,InfD,SupD) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [V] :
( ~ completion_compatible(V,ninf,nsup)
| ~ leq(V,nsup)
| ~ leq(ninf,V) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
! [V] :
( ~ completion_compatible(V,ninf,nsup)
| ~ leq(V,nsup)
| ~ leq(ninf,V) ),
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
leq(X,nsup),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
leq(X_447,nsup),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_447))]]) ).
cnf(refute_0_2,plain,
leq(ninf,X),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
leq(ninf,X_444),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_444))]]) ).
cnf(refute_0_4,plain,
( ~ leq(InfD,V)
| ~ leq(V,SupD)
| completion_compatible(V,InfD,SupD) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ leq(X_444,X_443)
| ~ leq(ninf,X_444)
| completion_compatible(X_444,ninf,X_443) ),
inference(subst,[],[refute_0_4:[bind(InfD,$fot(ninf)),bind(SupD,$fot(X_443)),bind(V,$fot(X_444))]]) ).
cnf(refute_0_6,plain,
( ~ leq(X_444,X_443)
| completion_compatible(X_444,ninf,X_443) ),
inference(resolve,[$cnf( leq(ninf,X_444) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ leq(X_447,nsup)
| completion_compatible(X_447,ninf,nsup) ),
inference(subst,[],[refute_0_6:[bind(X_443,$fot(nsup)),bind(X_444,$fot(X_447))]]) ).
cnf(refute_0_8,plain,
completion_compatible(X_447,ninf,nsup),
inference(resolve,[$cnf( leq(X_447,nsup) )],[refute_0_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ completion_compatible(V,ninf,nsup)
| ~ leq(V,nsup)
| ~ leq(ninf,V) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_10,plain,
leq(V,nsup),
inference(subst,[],[refute_0_0:[bind(X,$fot(V))]]) ).
cnf(refute_0_11,plain,
( ~ completion_compatible(V,ninf,nsup)
| ~ leq(ninf,V) ),
inference(resolve,[$cnf( leq(V,nsup) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
leq(ninf,V),
inference(subst,[],[refute_0_2:[bind(X,$fot(V))]]) ).
cnf(refute_0_13,plain,
~ completion_compatible(V,ninf,nsup),
inference(resolve,[$cnf( leq(ninf,V) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
~ completion_compatible(X_447,ninf,nsup),
inference(subst,[],[refute_0_13:[bind(V,$fot(X_447))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( completion_compatible(X_447,ninf,nsup) )],[refute_0_8,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 7 13:51:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 119.84/120.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 119.84/120.17
% 119.84/120.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.84/120.17
%------------------------------------------------------------------------------