%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT090+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n001.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 06:16:17 AM UTC 2026
% Result : Theorem 0.45s 0.75s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 20 unt; 0 def)
% Number of atoms : 106 ( 27 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 111 ( 54 ~; 38 |; 11 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 54 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_implies_leq,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ) ).
fof(wf_eq,axiom,
! [V,InfD,SupD] :
( wf(eq,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD) ) ) ).
fof(wf_lt,axiom,
! [V,InfD,SupD] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& V != InfD ) ) ).
fof(ord_v0_v600,axiom,
less(v0,v600) ).
fof(ord_v600_v1200,axiom,
less(v600,v1200) ).
fof(distinct,axiom,
( v0 != v600
& v0 != v1200
& v600 != v1200 ) ).
fof(odrl613,conjecture,
wf(lt,v600,v0,v1200) ).
fof(subgoal_0,plain,
wf(lt,v600,v0,v1200),
inference(strip,[],[odrl613]) ).
fof(negate_0_0,plain,
~ wf(lt,v600,v0,v1200),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [InfD,SupD,V] :
( ~ wf(lt,V,InfD,SupD)
<=> ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| V = InfD ) ),
inference(canonicalize,[],[wf_lt]) ).
fof(normalize_0_1,plain,
! [InfD,SupD,V] :
( ~ wf(eq,V,InfD,SupD)
<=> ( ~ leq(InfD,V)
| ~ leq(V,SupD) ) ),
inference(canonicalize,[],[wf_eq]) ).
fof(normalize_0_2,plain,
! [InfD,SupD,V] :
( ~ wf(eq,V,InfD,SupD)
<=> ( ~ leq(InfD,V)
| ~ leq(V,SupD) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [InfD,SupD,V] :
( ~ wf(lt,V,InfD,SupD)
<=> ( ~ wf(eq,V,InfD,SupD)
| V = InfD ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
! [InfD,SupD,V] :
( ~ wf(lt,V,InfD,SupD)
<=> ( ~ wf(eq,V,InfD,SupD)
| V = InfD ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [InfD,SupD,V] :
( ( V != InfD
| ~ wf(lt,V,InfD,SupD) )
& ( ~ wf(lt,V,InfD,SupD)
| wf(eq,V,InfD,SupD) )
& ( ~ wf(eq,V,InfD,SupD)
| V = InfD
| wf(lt,V,InfD,SupD) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [InfD,SupD,V] :
( ~ wf(eq,V,InfD,SupD)
| V = InfD
| wf(lt,V,InfD,SupD) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
less(v0,v600),
inference(canonicalize,[],[ord_v0_v600]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
less(v600,v1200),
inference(canonicalize,[],[ord_v600_v1200]) ).
fof(normalize_0_11,plain,
! [InfD,SupD,V] :
( ( ~ wf(eq,V,InfD,SupD)
| leq(InfD,V) )
& ( ~ wf(eq,V,InfD,SupD)
| leq(V,SupD) )
& ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| wf(eq,V,InfD,SupD) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [InfD,SupD,V] :
( ~ leq(InfD,V)
| ~ leq(V,SupD)
| wf(eq,V,InfD,SupD) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( v0 != v1200
& v0 != v600
& v600 != v1200 ),
inference(canonicalize,[],[distinct]) ).
fof(normalize_0_14,plain,
v0 != v600,
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ wf(lt,v600,v0,v1200),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ wf(eq,V,InfD,SupD)
| V = InfD
| wf(lt,V,InfD,SupD) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ wf(eq,v600,v0,v1200)
| v600 = v0
| wf(lt,v600,v0,v1200) ),
inference(subst,[],[refute_0_0:[bind(InfD,$fot(v0)),bind(SupD,$fot(v1200)),bind(V,$fot(v600))]]) ).
cnf(refute_0_2,plain,
less(v0,v600),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ less(v0,v600)
| leq(v0,v600) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(v0)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_5,plain,
leq(v0,v600),
inference(resolve,[$cnf( less(v0,v600) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
less(v600,v1200),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ less(v600,v1200)
| leq(v600,v1200) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(v600)),bind(Y,$fot(v1200))]]) ).
cnf(refute_0_8,plain,
leq(v600,v1200),
inference(resolve,[$cnf( less(v600,v1200) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ leq(InfD,V)
| ~ leq(V,SupD)
| wf(eq,V,InfD,SupD) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ leq(X_449,v600)
| ~ leq(v600,v1200)
| wf(eq,v600,X_449,v1200) ),
inference(subst,[],[refute_0_9:[bind(InfD,$fot(X_449)),bind(SupD,$fot(v1200)),bind(V,$fot(v600))]]) ).
cnf(refute_0_11,plain,
( ~ leq(X_449,v600)
| wf(eq,v600,X_449,v1200) ),
inference(resolve,[$cnf( leq(v600,v1200) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ leq(v0,v600)
| wf(eq,v600,v0,v1200) ),
inference(subst,[],[refute_0_11:[bind(X_449,$fot(v0))]]) ).
cnf(refute_0_13,plain,
wf(eq,v600,v0,v1200),
inference(resolve,[$cnf( leq(v0,v600) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
( v600 = v0
| wf(lt,v600,v0,v1200) ),
inference(resolve,[$cnf( wf(eq,v600,v0,v1200) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
v0 != v600,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( v600 != v0
| v0 = v600 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(v600)),bind(Y0,$fot(v0))]]) ).
cnf(refute_0_20,plain,
v600 != v0,
inference(resolve,[$cnf( $equal(v0,v600) )],[refute_0_19,refute_0_15]) ).
cnf(refute_0_21,plain,
wf(lt,v600,v0,v1200),
inference(resolve,[$cnf( $equal(v600,v0) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
~ wf(lt,v600,v0,v1200),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( wf(lt,v600,v0,v1200) )],[refute_0_21,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT090+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.11/0.36 % Computer : n001.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
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 7 14:27:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.45/0.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.75
% 0.45/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.45/0.75
%------------------------------------------------------------------------------