TSTP Solution File: SWV134+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV134+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 20:30:14 EDT 2022
% Result : Theorem 12.92s 13.09s
% Output : CNFRefutation 12.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 20 unt; 0 def)
% Number of atoms : 144 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 135 ( 49 ~; 33 |; 43 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ).
fof(leq_succ_succ,axiom,
! [X,Y] :
( leq(succ(X),succ(Y))
<=> leq(X,Y) ) ).
fof(gauss_array_0004,conjecture,
( ( ~ leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_worst7))
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_sworst7)) )
=> leq(n0,pv1325) ) ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(successor_2,axiom,
succ(succ(n0)) = n2 ).
fof(subgoal_0,plain,
( ( ~ leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_worst7))
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_sworst7)) )
=> leq(n0,pv1325) ),
inference(strip,[],[gauss_array_0004]) ).
fof(negate_0_0,plain,
~ ( ( ~ leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_worst7))
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_sworst7)) )
=> leq(n0,pv1325) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[leq_gt1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(canonicalize,[],[leq_succ_gt_equiv]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( ~ leq(X,Y)
| gt(succ(Y),X) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ~ leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_worst7))
& ~ leq(n0,pv1325)
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_sworst7))
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(pv1325,n3)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
leq(n2,pv1325),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[leq_succ_succ]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( ~ leq(succ(X),succ(Y))
| leq(X,Y) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[successor_2]) ).
fof(normalize_0_13,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_0_14,plain,
~ leq(n0,pv1325),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ gt(succ(succ(pv1325)),n2)
| leq(n2,succ(succ(pv1325))) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(n2)),bind(Y,$fot(succ(succ(pv1325))))]]) ).
cnf(refute_0_2,plain,
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ leq(n2,succ(pv1325))
| gt(succ(succ(pv1325)),n2) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(n2)),bind(Y,$fot(succ(pv1325)))]]) ).
cnf(refute_0_4,plain,
( ~ gt(succ(pv1325),n2)
| leq(n2,succ(pv1325)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(n2)),bind(Y,$fot(succ(pv1325)))]]) ).
cnf(refute_0_5,plain,
leq(n2,pv1325),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ leq(n2,pv1325)
| gt(succ(pv1325),n2) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(n2)),bind(Y,$fot(pv1325))]]) ).
cnf(refute_0_7,plain,
gt(succ(pv1325),n2),
inference(resolve,[$cnf( leq(n2,pv1325) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
leq(n2,succ(pv1325)),
inference(resolve,[$cnf( gt(succ(pv1325),n2) )],[refute_0_7,refute_0_4]) ).
cnf(refute_0_9,plain,
gt(succ(succ(pv1325)),n2),
inference(resolve,[$cnf( leq(n2,succ(pv1325)) )],[refute_0_8,refute_0_3]) ).
cnf(refute_0_10,plain,
leq(n2,succ(succ(pv1325))),
inference(resolve,[$cnf( gt(succ(succ(pv1325)),n2) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ leq(succ(n1),succ(X_688))
| leq(n1,X_688) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(n1)),bind(Y,$fot(X_688))]]) ).
cnf(refute_0_13,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
succ(succ(n0)) = succ(succ(n0)),
introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).
cnf(refute_0_16,plain,
( succ(n0) != n1
| succ(succ(n0)) != succ(succ(n0))
| succ(succ(n0)) = succ(n1) ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) ),[1,0],$fot(n1)]]) ).
cnf(refute_0_17,plain,
( succ(n0) != n1
| succ(succ(n0)) = succ(n1) ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
succ(succ(n0)) = succ(n1),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( succ(succ(n0)) != n2
| succ(succ(n0)) != succ(n1)
| succ(n1) = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),n2) ),[0],$fot(succ(n1))]]) ).
cnf(refute_0_20,plain,
( succ(succ(n0)) != n2
| succ(n1) = n2 ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
succ(n1) = n2,
inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
( succ(n1) != n2
| ~ leq(n2,succ(X_688))
| leq(succ(n1),succ(X_688)) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(n1),succ(X_688)) ),[0],$fot(n2)]]) ).
cnf(refute_0_23,plain,
( ~ leq(n2,succ(X_688))
| leq(succ(n1),succ(X_688)) ),
inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ leq(n2,succ(X_688))
| leq(n1,X_688) ),
inference(resolve,[$cnf( leq(succ(n1),succ(X_688)) )],[refute_0_23,refute_0_12]) ).
cnf(refute_0_25,plain,
( ~ leq(n2,succ(succ(pv1325)))
| leq(n1,succ(pv1325)) ),
inference(subst,[],[refute_0_24:[bind(X_688,$fot(succ(pv1325)))]]) ).
cnf(refute_0_26,plain,
leq(n1,succ(pv1325)),
inference(resolve,[$cnf( leq(n2,succ(succ(pv1325))) )],[refute_0_10,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ leq(succ(n0),succ(X_688))
| leq(n0,X_688) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(n0)),bind(Y,$fot(X_688))]]) ).
cnf(refute_0_28,plain,
( succ(n0) != n1
| ~ leq(n1,succ(X_688))
| leq(succ(n0),succ(X_688)) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(n0),succ(X_688)) ),[0],$fot(n1)]]) ).
cnf(refute_0_29,plain,
( ~ leq(n1,succ(X_688))
| leq(succ(n0),succ(X_688)) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ leq(n1,succ(X_688))
| leq(n0,X_688) ),
inference(resolve,[$cnf( leq(succ(n0),succ(X_688)) )],[refute_0_29,refute_0_27]) ).
cnf(refute_0_31,plain,
( ~ leq(n1,succ(pv1325))
| leq(n0,pv1325) ),
inference(subst,[],[refute_0_30:[bind(X_688,$fot(pv1325))]]) ).
cnf(refute_0_32,plain,
leq(n0,pv1325),
inference(resolve,[$cnf( leq(n1,succ(pv1325)) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
~ leq(n0,pv1325),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( leq(n0,pv1325) )],[refute_0_32,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV134+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 01:29:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 12.92/13.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.92/13.09
% 12.92/13.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.92/13.09
%------------------------------------------------------------------------------