TSTP Solution File: SWV056+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV056+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 20:29:58 EDT 2022
% Result : Theorem 0.76s 0.96s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 35 unt; 0 def)
% Number of atoms : 108 ( 79 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 82 ( 33 ~; 25 |; 17 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 23 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_plus_base,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0 ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0 ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X) ).
fof(pred_succ,axiom,
! [X] : pred(succ(X)) = X ).
fof(cl5_nebula_norm_0040,conjecture,
( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
=> ( n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ) ) ).
fof(subgoal_0,plain,
( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
=> n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
inference(strip,[],[cl5_nebula_norm_0040]) ).
fof(subgoal_1,plain,
( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1))
& n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
=> leq(n0,pv25) ),
inference(strip,[],[cl5_nebula_norm_0040]) ).
fof(subgoal_2,plain,
( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1))
& n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))
& leq(n0,pv25) )
=> leq(pv25,minus(n5,n1)) ),
inference(strip,[],[cl5_nebula_norm_0040]) ).
fof(negate_0_0,plain,
~ ( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1)) )
=> n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))
& leq(n0,pv25)
& leq(pv25,minus(n5,n1)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : minus(X,n1) = pred(X),
inference(canonicalize,[],[pred_minus_1]) ).
fof(normalize_0_3,plain,
! [X] : minus(X,n1) = pred(X),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
inference(canonicalize,[],[sum_plus_base]) ).
fof(normalize_0_5,plain,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : pred(succ(X)) = X,
inference(canonicalize,[],[pred_succ]) ).
fof(normalize_0_7,plain,
! [X] : pred(succ(X)) = X,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
succ(tptp_minus_1) = n0,
inference(canonicalize,[],[succ_tptp_minus_1]) ).
cnf(refute_0_0,plain,
n0 != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
minus(X,n1) = pred(X),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
minus(n0,n1) = pred(n0),
inference(subst,[],[refute_0_1:[bind(X,$fot(n0))]]) ).
cnf(refute_0_3,plain,
sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),
introduced(tautology,[refl,[$fot(sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)))]]) ).
cnf(refute_0_4,plain,
( minus(n0,n1) != pred(n0)
| sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) != sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))
| sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) = sum(n0,pred(n0),a_select3(q,pv77,pv25)) ),
introduced(tautology,[equality,[$cnf( $equal(sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))) ),[1,1],$fot(pred(n0))]]) ).
cnf(refute_0_5,plain,
( minus(n0,n1) != pred(n0)
| sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) = sum(n0,pred(n0),a_select3(q,pv77,pv25)) ),
inference(resolve,[$cnf( $equal(sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) = sum(n0,pred(n0),a_select3(q,pv77,pv25)),
inference(resolve,[$cnf( $equal(minus(n0,n1),pred(n0)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( n0 != sum(n0,pred(n0),a_select3(q,pv77,pv25))
| sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) != sum(n0,pred(n0),a_select3(q,pv77,pv25))
| n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(n0,sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))) ),[1],$fot(sum(n0,pred(n0),a_select3(q,pv77,pv25)))]]) ).
cnf(refute_0_8,plain,
( n0 != sum(n0,pred(n0),a_select3(q,pv77,pv25))
| n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) ),
inference(resolve,[$cnf( $equal(sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)),sum(n0,pred(n0),a_select3(q,pv77,pv25))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
n0 != sum(n0,pred(n0),a_select3(q,pv77,pv25)),
inference(resolve,[$cnf( $equal(n0,sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
sum(n0,tptp_minus_1,Body) = n0,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_11,plain,
sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) = n0,
inference(subst,[],[refute_0_10:[bind(Body,$fot(a_select3(q,pv77,pv25)))]]) ).
cnf(refute_0_12,plain,
pred(succ(X)) = X,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_13,plain,
pred(succ(tptp_minus_1)) = tptp_minus_1,
inference(subst,[],[refute_0_12:[bind(X,$fot(tptp_minus_1))]]) ).
cnf(refute_0_14,plain,
succ(tptp_minus_1) = n0,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_15,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| succ(tptp_minus_1) != n0
| pred(n0) = tptp_minus_1 ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) ),[0,0],$fot(n0)]]) ).
cnf(refute_0_16,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| pred(n0) = tptp_minus_1 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
pred(n0) = tptp_minus_1,
inference(resolve,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
sum(n0,pred(n0),a_select3(q,pv77,pv25)) = sum(n0,pred(n0),a_select3(q,pv77,pv25)),
introduced(tautology,[refl,[$fot(sum(n0,pred(n0),a_select3(q,pv77,pv25)))]]) ).
cnf(refute_0_19,plain,
( pred(n0) != tptp_minus_1
| sum(n0,pred(n0),a_select3(q,pv77,pv25)) != sum(n0,pred(n0),a_select3(q,pv77,pv25))
| sum(n0,pred(n0),a_select3(q,pv77,pv25)) = sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) ),
introduced(tautology,[equality,[$cnf( $equal(sum(n0,pred(n0),a_select3(q,pv77,pv25)),sum(n0,pred(n0),a_select3(q,pv77,pv25))) ),[1,1],$fot(tptp_minus_1)]]) ).
cnf(refute_0_20,plain,
( pred(n0) != tptp_minus_1
| sum(n0,pred(n0),a_select3(q,pv77,pv25)) = sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),a_select3(q,pv77,pv25)),sum(n0,pred(n0),a_select3(q,pv77,pv25))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
sum(n0,pred(n0),a_select3(q,pv77,pv25)) = sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)),
inference(resolve,[$cnf( $equal(pred(n0),tptp_minus_1) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( sum(n0,pred(n0),a_select3(q,pv77,pv25)) != sum(n0,tptp_minus_1,a_select3(q,pv77,pv25))
| sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) != n0
| sum(n0,pred(n0),a_select3(q,pv77,pv25)) = n0 ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(sum(n0,pred(n0),a_select3(q,pv77,pv25)))),bind(Y,$fot(sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_28,plain,
( sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)) != n0
| sum(n0,pred(n0),a_select3(q,pv77,pv25)) = n0 ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),a_select3(q,pv77,pv25)),sum(n0,tptp_minus_1,a_select3(q,pv77,pv25))) )],[refute_0_21,refute_0_27]) ).
cnf(refute_0_29,plain,
sum(n0,pred(n0),a_select3(q,pv77,pv25)) = n0,
inference(resolve,[$cnf( $equal(sum(n0,tptp_minus_1,a_select3(q,pv77,pv25)),n0) )],[refute_0_11,refute_0_28]) ).
cnf(refute_0_30,plain,
( n0 != n0
| sum(n0,pred(n0),a_select3(q,pv77,pv25)) != n0
| n0 = sum(n0,pred(n0),a_select3(q,pv77,pv25)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(n0,sum(n0,pred(n0),a_select3(q,pv77,pv25))) ),[1],$fot(n0)]]) ).
cnf(refute_0_31,plain,
( n0 != n0
| n0 = sum(n0,pred(n0),a_select3(q,pv77,pv25)) ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),a_select3(q,pv77,pv25)),n0) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
n0 != n0,
inference(resolve,[$cnf( $equal(n0,sum(n0,pred(n0),a_select3(q,pv77,pv25))) )],[refute_0_31,refute_0_9]) ).
cnf(refute_0_33,plain,
n0 = n0,
introduced(tautology,[refl,[$fot(n0)]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_33,refute_0_32]) ).
fof(negate_1_0,plain,
~ ( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1))
& n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25)) )
=> leq(n0,pv25) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
$false,
inference(canonicalize,[],[negate_1_0]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_0]) ).
fof(negate_2_0,plain,
~ ( ( leq(n0,pv25)
& leq(pv25,minus(n5,n1))
& n0 = sum(n0,minus(n0,n1),a_select3(q,pv77,pv25))
& leq(n0,pv25) )
=> leq(pv25,minus(n5,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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV056+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 19:23:24 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.76/0.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/0.96
% 0.76/0.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.76/0.97
%------------------------------------------------------------------------------