%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV067+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:30:01 EDT 2022
% Result : Theorem 2.35s 2.53s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 226 ( 4 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 206 ( 38 ~; 14 |; 127 &)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ) ).
fof(leq_succ_succ,axiom,
! [X,Y] :
( leq(succ(X),succ(Y))
<=> leq(X,Y) ) ).
fof(cl5_nebula_array_0008,conjecture,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
=> ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) ) ) ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(subgoal_0,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
=> leq(n0,pv10) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_1,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10) )
=> leq(n0,pv63) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_2,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63) )
=> leq(pv10,minus(n135300,n1)) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_3,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1)) )
=> leq(pv63,minus(n5,n1)) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_4,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ~ gt(a_select3(q,pv10,pv63),pv78) )
=> leq(n0,pv10) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_5,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ~ gt(a_select3(q,pv10,pv63),pv78)
& leq(n0,pv10) )
=> leq(pv10,minus(n135300,n1)) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_6,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& gt(a_select3(q,pv10,pv63),pv78) )
=> leq(n0,pv10) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(subgoal_7,plain,
( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& gt(a_select3(q,pv10,pv63),pv78)
& leq(n0,pv10) )
=> leq(pv10,minus(n135300,n1)) ),
inference(strip,[],[cl5_nebula_array_0008]) ).
fof(negate_0_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
=> leq(n0,pv10) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
$false,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_0]) ).
fof(negate_1_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10) )
=> leq(n0,pv63) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[leq_succ_succ]) ).
fof(normalize_1_1,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( ~ leq(succ(X),succ(Y))
| leq(X,Y) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [X,Y] :
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_1_5,plain,
( ~ leq(n0,pv63)
& leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_6,plain,
leq(n1,pv63),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(canonicalize,[],[leq_succ]) ).
fof(normalize_1_8,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
~ leq(n0,pv63),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ leq(succ(n0),succ(X_279))
| leq(n0,X_279) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(n0)),bind(Y,$fot(X_279))]]) ).
cnf(refute_1_2,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
( succ(n0) != n1
| ~ leq(n1,succ(X_279))
| leq(succ(n0),succ(X_279)) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(n0),succ(X_279)) ),[0],$fot(n1)]]) ).
cnf(refute_1_4,plain,
( ~ leq(n1,succ(X_279))
| leq(succ(n0),succ(X_279)) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( ~ leq(n1,succ(X_279))
| leq(n0,X_279) ),
inference(resolve,[$cnf( leq(succ(n0),succ(X_279)) )],[refute_1_4,refute_1_1]) ).
cnf(refute_1_6,plain,
( ~ leq(n1,succ(pv63))
| leq(n0,pv63) ),
inference(subst,[],[refute_1_5:[bind(X_279,$fot(pv63))]]) ).
cnf(refute_1_7,plain,
leq(n1,pv63),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_8,plain,
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_9,plain,
( ~ leq(n1,pv63)
| leq(n1,succ(pv63)) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(n1)),bind(Y,$fot(pv63))]]) ).
cnf(refute_1_10,plain,
leq(n1,succ(pv63)),
inference(resolve,[$cnf( leq(n1,pv63) )],[refute_1_7,refute_1_9]) ).
cnf(refute_1_11,plain,
leq(n0,pv63),
inference(resolve,[$cnf( leq(n1,succ(pv63)) )],[refute_1_10,refute_1_6]) ).
cnf(refute_1_12,plain,
~ leq(n0,pv63),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_13,plain,
$false,
inference(resolve,[$cnf( leq(n0,pv63) )],[refute_1_11,refute_1_12]) ).
fof(negate_2_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63) )
=> leq(pv10,minus(n135300,n1)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
$false,
inference(canonicalize,[],[negate_2_0]) ).
cnf(refute_2_0,plain,
$false,
inference(canonicalize,[],[normalize_2_0]) ).
fof(negate_3_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1)) )
=> leq(pv63,minus(n5,n1)) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
$false,
inference(canonicalize,[],[negate_3_0]) ).
cnf(refute_3_0,plain,
$false,
inference(canonicalize,[],[normalize_3_0]) ).
fof(negate_4_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ~ gt(a_select3(q,pv10,pv63),pv78) )
=> leq(n0,pv10) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
$false,
inference(canonicalize,[],[negate_4_0]) ).
cnf(refute_4_0,plain,
$false,
inference(canonicalize,[],[normalize_4_0]) ).
fof(negate_5_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ~ gt(a_select3(q,pv10,pv63),pv78)
& leq(n0,pv10) )
=> leq(pv10,minus(n135300,n1)) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
$false,
inference(canonicalize,[],[negate_5_0]) ).
cnf(refute_5_0,plain,
$false,
inference(canonicalize,[],[normalize_5_0]) ).
fof(negate_6_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& gt(a_select3(q,pv10,pv63),pv78) )
=> leq(n0,pv10) ),
inference(negate,[],[subgoal_6]) ).
fof(normalize_6_0,plain,
$false,
inference(canonicalize,[],[negate_6_0]) ).
cnf(refute_6_0,plain,
$false,
inference(canonicalize,[],[normalize_6_0]) ).
fof(negate_7_0,plain,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& gt(a_select3(q,pv10,pv63),pv78)
& leq(n0,pv10) )
=> leq(pv10,minus(n135300,n1)) ),
inference(negate,[],[subgoal_7]) ).
fof(normalize_7_0,plain,
$false,
inference(canonicalize,[],[negate_7_0]) ).
cnf(refute_7_0,plain,
$false,
inference(canonicalize,[],[normalize_7_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV067+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 21:30:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.35/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.35/2.53
% 2.35/2.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.35/2.54
%------------------------------------------------------------------------------