%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT073+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 22 |; 10 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 78 ( 0 sgn 52 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axis_conflict_def,axiom,
! [I1lo,I1hi,I2lo,I2hi] :
( axis_conflict(I1lo,I1hi,I2lo,I2hi)
<=> ~ ? [X] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) ).
fof(axis_compatible_def,axiom,
! [I1lo,I1hi,I2lo,I2hi] :
( axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ? [X] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) ).
fof(compatible_hyp,hypothesis,
axis_compatible(n0,n10,n5,n10) ).
fof(no_false_compatible,conjecture,
? [X] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ) ).
fof(subgoal_0,plain,
? [X] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(strip,[],[no_false_compatible]) ).
fof(negate_0_0,plain,
~ ? [X] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ~ axis_conflict(I1lo,I1hi,I2lo,I2hi)
<=> ? [X] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ),
inference(canonicalize,[],[axis_conflict_def]) ).
fof(normalize_0_1,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ~ axis_conflict(I1lo,I1hi,I2lo,I2hi)
<=> ? [X] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [I1hi,I1lo,I2hi,I2lo,X] :
( ( axis_conflict(I1lo,I1hi,I2lo,I2hi)
| in_closed(skolemFOFtoCNF_X(I1hi,I1lo,I2hi,I2lo),I1lo,I1hi) )
& ( axis_conflict(I1lo,I1hi,I2lo,I2hi)
| in_closed(skolemFOFtoCNF_X(I1hi,I1lo,I2hi,I2lo),I2lo,I2hi) )
& ( ~ axis_conflict(I1lo,I1hi,I2lo,I2hi)
| ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( axis_conflict(I1lo,I1hi,I2lo,I2hi)
| in_closed(skolemFOFtoCNF_X(I1hi,I1lo,I2hi,I2lo),I1lo,I1hi) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( axis_conflict(I1lo,I1hi,I2lo,I2hi)
| in_closed(skolemFOFtoCNF_X(I1hi,I1lo,I2hi,I2lo),I2lo,I2hi) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ! [X] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ),
inference(canonicalize,[],[axis_compatible_def]) ).
fof(normalize_0_8,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> axis_conflict(I1lo,I1hi,I2lo,I2hi) ),
inference(simplify,[],[normalize_0_7,normalize_0_1]) ).
fof(normalize_0_9,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> axis_conflict(I1lo,I1hi,I2lo,I2hi) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ axis_conflict(I1lo,I1hi,I2lo,I2hi) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| axis_conflict(I1lo,I1hi,I2lo,I2hi) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [I1hi,I1lo,I2hi,I2lo] :
( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ axis_conflict(I1lo,I1hi,I2lo,I2hi) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
axis_compatible(n0,n10,n5,n10),
inference(canonicalize,[],[compatible_hyp]) ).
cnf(refute_0_0,plain,
( axis_conflict(I1lo,I1hi,I2lo,I2hi)
| in_closed(skolemFOFtoCNF_X(I1hi,I1lo,I2hi,I2lo),I1lo,I1hi) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( axis_conflict(n0,n10,n5,n10)
| in_closed(skolemFOFtoCNF_X(n10,n0,n10,n5),n0,n10) ),
inference(subst,[],[refute_0_0:[bind(I1hi,$fot(n10)),bind(I1lo,$fot(n0)),bind(I2hi,$fot(n10)),bind(I2lo,$fot(n5))]]) ).
cnf(refute_0_2,plain,
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ in_closed(skolemFOFtoCNF_X(X_43,X_44,n10,n5),n0,n10)
| ~ in_closed(skolemFOFtoCNF_X(X_43,X_44,n10,n5),n5,n10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X(X_43,X_44,n10,n5)))]]) ).
cnf(refute_0_4,plain,
( axis_conflict(I1lo,I1hi,I2lo,I2hi)
| in_closed(skolemFOFtoCNF_X(I1hi,I1lo,I2hi,I2lo),I2lo,I2hi) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( axis_conflict(X_44,X_43,n5,n10)
| in_closed(skolemFOFtoCNF_X(X_43,X_44,n10,n5),n5,n10) ),
inference(subst,[],[refute_0_4:[bind(I1hi,$fot(X_43)),bind(I1lo,$fot(X_44)),bind(I2hi,$fot(n10)),bind(I2lo,$fot(n5))]]) ).
cnf(refute_0_6,plain,
( ~ in_closed(skolemFOFtoCNF_X(X_43,X_44,n10,n5),n0,n10)
| axis_conflict(X_44,X_43,n5,n10) ),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X(X_43,X_44,n10,n5),n5,n10) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( ~ in_closed(skolemFOFtoCNF_X(n10,n0,n10,n5),n0,n10)
| axis_conflict(n0,n10,n5,n10) ),
inference(subst,[],[refute_0_6:[bind(X_43,$fot(n10)),bind(X_44,$fot(n0))]]) ).
cnf(refute_0_8,plain,
axis_conflict(n0,n10,n5,n10),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X(n10,n0,n10,n5),n0,n10) )],[refute_0_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ axis_conflict(I1lo,I1hi,I2lo,I2hi) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
( ~ axis_compatible(n0,n10,n5,n10)
| ~ axis_conflict(n0,n10,n5,n10) ),
inference(subst,[],[refute_0_9:[bind(I1hi,$fot(n10)),bind(I1lo,$fot(n0)),bind(I2hi,$fot(n10)),bind(I2lo,$fot(n5))]]) ).
cnf(refute_0_11,plain,
~ axis_compatible(n0,n10,n5,n10),
inference(resolve,[$cnf( axis_conflict(n0,n10,n5,n10) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
axis_compatible(n0,n10,n5,n10),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( axis_compatible(n0,n10,n5,n10) )],[refute_0_12,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT073+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 7 13:57:07 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45
% 0.12/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.45
%------------------------------------------------------------------------------