TSTP Solution File: SWV069+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV069+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 1.04s 1.22s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 28
% Syntax : Number of formulae : 172 ( 101 unt; 0 def)
% Number of atoms : 295 ( 207 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 219 ( 96 ~; 84 |; 29 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_leq,axiom,
! [X] : leq(X,X) ).
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ) ).
fof(succ_plus_1_l,axiom,
! [X] : plus(n1,X) = succ(X) ).
fof(succ_plus_3_r,axiom,
! [X] : plus(X,n3) = succ(succ(succ(X))) ).
fof(succ_plus_3_l,axiom,
! [X] : plus(n3,X) = succ(succ(succ(X))) ).
fof(succ_plus_4_r,axiom,
! [X] : plus(X,n4) = succ(succ(succ(succ(X)))) ).
fof(succ_plus_4_l,axiom,
! [X] : plus(n4,X) = succ(succ(succ(succ(X)))) ).
fof(succ_plus_5_r,axiom,
! [X] : plus(X,n5) = succ(succ(succ(succ(succ(X))))) ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X) ).
fof(pred_succ,axiom,
! [X] : pred(succ(X)) = X ).
fof(cl5_nebula_array_0010,conjecture,
( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ) ) ).
fof(gt_4_0,axiom,
gt(n4,n0) ).
fof(successor_5,axiom,
succ(succ(succ(succ(succ(n0))))) = n5 ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(subgoal_0,plain,
( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
=> leq(n0,n0) ),
inference(strip,[],[cl5_nebula_array_0010]) ).
fof(subgoal_1,plain,
( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& leq(n0,n0) )
=> leq(n0,pv10) ),
inference(strip,[],[cl5_nebula_array_0010]) ).
fof(subgoal_2,plain,
( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& leq(n0,n0)
& leq(n0,pv10) )
=> leq(n0,minus(n5,n1)) ),
inference(strip,[],[cl5_nebula_array_0010]) ).
fof(subgoal_3,plain,
( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1)) )
=> leq(pv10,minus(n135300,n1)) ),
inference(strip,[],[cl5_nebula_array_0010]) ).
fof(negate_0_0,plain,
~ ( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
=> leq(n0,n0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ leq(n0,n0)
& leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ leq(n0,n0),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : leq(X,X),
inference(canonicalize,[],[reflexivity_leq]) ).
fof(normalize_0_3,plain,
! [X] : leq(X,X),
inference(specialize,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
~ leq(n0,n0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
leq(X,X),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
leq(n0,n0),
inference(subst,[],[refute_0_1:[bind(X,$fot(n0))]]) ).
cnf(refute_0_3,plain,
$false,
inference(resolve,[$cnf( leq(n0,n0) )],[refute_0_2,refute_0_0]) ).
fof(negate_1_0,plain,
~ ( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& leq(n0,n0) )
=> leq(n0,pv10) ),
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,pv10)
& leq(pv10,minus(n135300,n1))
& leq(n0,n0)
& leq(n0,pv10) )
=> leq(n0,minus(n5,n1)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
gt(n4,n0),
inference(canonicalize,[],[gt_4_0]) ).
fof(normalize_2_1,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[leq_gt1]) ).
fof(normalize_2_2,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ leq(n0,minus(n5,n1))
& leq(n0,n0)
& leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_4,plain,
~ leq(n0,minus(n5,n1)),
inference(conjunct,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [X] : minus(X,n1) = pred(X),
inference(canonicalize,[],[pred_minus_1]) ).
fof(normalize_2_6,plain,
! [X] : minus(X,n1) = pred(X),
inference(specialize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [X] : pred(succ(X)) = X,
inference(canonicalize,[],[pred_succ]) ).
fof(normalize_2_8,plain,
! [X] : pred(succ(X)) = X,
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [X] : plus(X,n5) = succ(succ(succ(succ(succ(X))))),
inference(canonicalize,[],[succ_plus_5_r]) ).
fof(normalize_2_10,plain,
! [X] : plus(X,n5) = succ(succ(succ(succ(succ(X))))),
inference(specialize,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [X] : plus(n4,X) = succ(succ(succ(succ(X)))),
inference(canonicalize,[],[succ_plus_4_l]) ).
fof(normalize_2_12,plain,
! [X] : plus(n4,X) = succ(succ(succ(succ(X)))),
inference(specialize,[],[normalize_2_11]) ).
fof(normalize_2_13,plain,
! [X] : plus(X,n4) = succ(succ(succ(succ(X)))),
inference(canonicalize,[],[succ_plus_4_r]) ).
fof(normalize_2_14,plain,
! [X] : plus(X,n4) = succ(succ(succ(succ(X)))),
inference(specialize,[],[normalize_2_13]) ).
fof(normalize_2_15,plain,
! [X] : plus(n3,X) = succ(succ(succ(X))),
inference(canonicalize,[],[succ_plus_3_l]) ).
fof(normalize_2_16,plain,
! [X] : plus(n3,X) = succ(succ(succ(X))),
inference(specialize,[],[normalize_2_15]) ).
fof(normalize_2_17,plain,
! [X] : plus(X,n3) = succ(succ(succ(X))),
inference(canonicalize,[],[succ_plus_3_r]) ).
fof(normalize_2_18,plain,
! [X] : plus(X,n3) = succ(succ(succ(X))),
inference(specialize,[],[normalize_2_17]) ).
fof(normalize_2_19,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_2_20,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(canonicalize,[],[successor_5]) ).
fof(normalize_2_21,plain,
! [X] : plus(n1,X) = succ(X),
inference(canonicalize,[],[succ_plus_1_l]) ).
fof(normalize_2_22,plain,
! [X] : plus(n1,X) = succ(X),
inference(specialize,[],[normalize_2_21]) ).
cnf(refute_2_0,plain,
gt(n4,n0),
inference(canonicalize,[],[normalize_2_0]) ).
cnf(refute_2_1,plain,
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_2,plain,
( ~ gt(n4,n0)
| leq(n0,n4) ),
inference(subst,[],[refute_2_1:[bind(X,$fot(n0)),bind(Y,$fot(n4))]]) ).
cnf(refute_2_3,plain,
leq(n0,n4),
inference(resolve,[$cnf( gt(n4,n0) )],[refute_2_0,refute_2_2]) ).
cnf(refute_2_4,plain,
~ leq(n0,minus(n5,n1)),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_5,plain,
minus(X,n1) = pred(X),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_6,plain,
minus(n5,n1) = pred(n5),
inference(subst,[],[refute_2_5:[bind(X,$fot(n5))]]) ).
cnf(refute_2_7,plain,
( minus(n5,n1) != pred(n5)
| ~ leq(n0,pred(n5))
| leq(n0,minus(n5,n1)) ),
introduced(tautology,[equality,[$cnf( ~ leq(n0,minus(n5,n1)) ),[1],$fot(pred(n5))]]) ).
cnf(refute_2_8,plain,
( ~ leq(n0,pred(n5))
| leq(n0,minus(n5,n1)) ),
inference(resolve,[$cnf( $equal(minus(n5,n1),pred(n5)) )],[refute_2_6,refute_2_7]) ).
cnf(refute_2_9,plain,
~ leq(n0,pred(n5)),
inference(resolve,[$cnf( leq(n0,minus(n5,n1)) )],[refute_2_8,refute_2_4]) ).
cnf(refute_2_10,plain,
pred(succ(X)) = X,
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_11,plain,
pred(succ(n4)) = n4,
inference(subst,[],[refute_2_10:[bind(X,$fot(n4))]]) ).
cnf(refute_2_12,plain,
plus(X,n5) = succ(succ(succ(succ(succ(X))))),
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_13,plain,
plus(n4,X) = succ(succ(succ(succ(X)))),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_14,plain,
plus(X,n4) = succ(succ(succ(succ(X)))),
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_15,plain,
plus(n3,X) = succ(succ(succ(X))),
inference(canonicalize,[],[normalize_2_16]) ).
cnf(refute_2_16,plain,
plus(X,n3) = succ(succ(succ(X))),
inference(canonicalize,[],[normalize_2_18]) ).
cnf(refute_2_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_2_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_2_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_2_17,refute_2_18]) ).
cnf(refute_2_20,plain,
( plus(X,n3) != succ(succ(succ(X)))
| succ(succ(succ(X))) = plus(X,n3) ),
inference(subst,[],[refute_2_19:[bind(X0,$fot(plus(X,n3))),bind(Y0,$fot(succ(succ(succ(X)))))]]) ).
cnf(refute_2_21,plain,
succ(succ(succ(X))) = plus(X,n3),
inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_2_16,refute_2_20]) ).
cnf(refute_2_22,plain,
( plus(n3,X) != succ(succ(succ(X)))
| succ(succ(succ(X))) != plus(X,n3)
| plus(n3,X) = plus(X,n3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(n3,X),plus(X,n3)) ),[0],$fot(succ(succ(succ(X))))]]) ).
cnf(refute_2_23,plain,
( plus(n3,X) != succ(succ(succ(X)))
| plus(n3,X) = plus(X,n3) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X))),plus(X,n3)) )],[refute_2_21,refute_2_22]) ).
cnf(refute_2_24,plain,
plus(n3,X) = plus(X,n3),
inference(resolve,[$cnf( $equal(plus(n3,X),succ(succ(succ(X)))) )],[refute_2_15,refute_2_23]) ).
cnf(refute_2_25,plain,
( plus(n3,X) != plus(X,n3)
| plus(X,n3) = plus(n3,X) ),
inference(subst,[],[refute_2_19:[bind(X0,$fot(plus(n3,X))),bind(Y0,$fot(plus(X,n3)))]]) ).
cnf(refute_2_26,plain,
plus(X,n3) = plus(n3,X),
inference(resolve,[$cnf( $equal(plus(n3,X),plus(X,n3)) )],[refute_2_24,refute_2_25]) ).
cnf(refute_2_27,plain,
plus(succ(X),n3) = plus(n3,succ(X)),
inference(subst,[],[refute_2_26:[bind(X,$fot(succ(X)))]]) ).
cnf(refute_2_28,plain,
succ(succ(succ(succ(X)))) = plus(succ(X),n3),
inference(subst,[],[refute_2_21:[bind(X,$fot(succ(X)))]]) ).
cnf(refute_2_29,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_2_30,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_2_19,refute_2_29]) ).
cnf(refute_2_31,plain,
( plus(succ(X),n3) != plus(n3,succ(X))
| succ(succ(succ(succ(X)))) != plus(succ(X),n3)
| succ(succ(succ(succ(X)))) = plus(n3,succ(X)) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(succ(succ(succ(succ(X)))))),bind(Y0,$fot(plus(succ(X),n3))),bind(Z,$fot(plus(n3,succ(X))))]]) ).
cnf(refute_2_32,plain,
( plus(succ(X),n3) != plus(n3,succ(X))
| succ(succ(succ(succ(X)))) = plus(n3,succ(X)) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(X)))),plus(succ(X),n3)) )],[refute_2_28,refute_2_31]) ).
cnf(refute_2_33,plain,
succ(succ(succ(succ(X)))) = plus(n3,succ(X)),
inference(resolve,[$cnf( $equal(plus(succ(X),n3),plus(n3,succ(X))) )],[refute_2_27,refute_2_32]) ).
cnf(refute_2_34,plain,
( plus(X,n4) != succ(succ(succ(succ(X))))
| succ(succ(succ(succ(X)))) != plus(n3,succ(X))
| plus(X,n4) = plus(n3,succ(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(X,n4),plus(n3,succ(X))) ),[0],$fot(succ(succ(succ(succ(X)))))]]) ).
cnf(refute_2_35,plain,
( plus(X,n4) != succ(succ(succ(succ(X))))
| plus(X,n4) = plus(n3,succ(X)) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(X)))),plus(n3,succ(X))) )],[refute_2_33,refute_2_34]) ).
cnf(refute_2_36,plain,
plus(X,n4) = plus(n3,succ(X)),
inference(resolve,[$cnf( $equal(plus(X,n4),succ(succ(succ(succ(X))))) )],[refute_2_14,refute_2_35]) ).
cnf(refute_2_37,plain,
( plus(X,n4) != plus(n3,succ(X))
| plus(n3,succ(X)) = plus(X,n4) ),
inference(subst,[],[refute_2_19:[bind(X0,$fot(plus(X,n4))),bind(Y0,$fot(plus(n3,succ(X))))]]) ).
cnf(refute_2_38,plain,
plus(n3,succ(X)) = plus(X,n4),
inference(resolve,[$cnf( $equal(plus(X,n4),plus(n3,succ(X))) )],[refute_2_36,refute_2_37]) ).
cnf(refute_2_39,plain,
( plus(n3,succ(X)) != plus(X,n4)
| plus(succ(X),n3) != plus(n3,succ(X))
| plus(succ(X),n3) = plus(X,n4) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(succ(X),n3))),bind(Y0,$fot(plus(n3,succ(X)))),bind(Z,$fot(plus(X,n4)))]]) ).
cnf(refute_2_40,plain,
( plus(n3,succ(X)) != plus(X,n4)
| plus(succ(X),n3) = plus(X,n4) ),
inference(resolve,[$cnf( $equal(plus(succ(X),n3),plus(n3,succ(X))) )],[refute_2_27,refute_2_39]) ).
cnf(refute_2_41,plain,
plus(succ(X),n3) = plus(X,n4),
inference(resolve,[$cnf( $equal(plus(n3,succ(X)),plus(X,n4)) )],[refute_2_38,refute_2_40]) ).
cnf(refute_2_42,plain,
( plus(succ(X),n3) != plus(X,n4)
| succ(succ(succ(succ(X)))) != plus(succ(X),n3)
| succ(succ(succ(succ(X)))) = plus(X,n4) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(succ(succ(succ(succ(X)))))),bind(Y0,$fot(plus(succ(X),n3))),bind(Z,$fot(plus(X,n4)))]]) ).
cnf(refute_2_43,plain,
( plus(succ(X),n3) != plus(X,n4)
| succ(succ(succ(succ(X)))) = plus(X,n4) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(X)))),plus(succ(X),n3)) )],[refute_2_28,refute_2_42]) ).
cnf(refute_2_44,plain,
succ(succ(succ(succ(X)))) = plus(X,n4),
inference(resolve,[$cnf( $equal(plus(succ(X),n3),plus(X,n4)) )],[refute_2_41,refute_2_43]) ).
cnf(refute_2_45,plain,
( plus(n4,X) != succ(succ(succ(succ(X))))
| succ(succ(succ(succ(X)))) != plus(X,n4)
| plus(n4,X) = plus(X,n4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(n4,X),plus(X,n4)) ),[0],$fot(succ(succ(succ(succ(X)))))]]) ).
cnf(refute_2_46,plain,
( plus(n4,X) != succ(succ(succ(succ(X))))
| plus(n4,X) = plus(X,n4) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(X)))),plus(X,n4)) )],[refute_2_44,refute_2_45]) ).
cnf(refute_2_47,plain,
plus(n4,X) = plus(X,n4),
inference(resolve,[$cnf( $equal(plus(n4,X),succ(succ(succ(succ(X))))) )],[refute_2_13,refute_2_46]) ).
cnf(refute_2_48,plain,
( plus(n4,X) != plus(X,n4)
| plus(X,n4) = plus(n4,X) ),
inference(subst,[],[refute_2_19:[bind(X0,$fot(plus(n4,X))),bind(Y0,$fot(plus(X,n4)))]]) ).
cnf(refute_2_49,plain,
plus(X,n4) = plus(n4,X),
inference(resolve,[$cnf( $equal(plus(n4,X),plus(X,n4)) )],[refute_2_47,refute_2_48]) ).
cnf(refute_2_50,plain,
plus(succ(X),n4) = plus(n4,succ(X)),
inference(subst,[],[refute_2_49:[bind(X,$fot(succ(X)))]]) ).
cnf(refute_2_51,plain,
plus(n3,succ(succ(X))) = plus(succ(X),n4),
inference(subst,[],[refute_2_38:[bind(X,$fot(succ(X)))]]) ).
cnf(refute_2_52,plain,
( plus(n3,succ(succ(X))) != plus(succ(X),n4)
| plus(succ(X),n4) != plus(n4,succ(X))
| plus(n3,succ(succ(X))) = plus(n4,succ(X)) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(n3,succ(succ(X))))),bind(Y0,$fot(plus(succ(X),n4))),bind(Z,$fot(plus(n4,succ(X))))]]) ).
cnf(refute_2_53,plain,
( plus(succ(X),n4) != plus(n4,succ(X))
| plus(n3,succ(succ(X))) = plus(n4,succ(X)) ),
inference(resolve,[$cnf( $equal(plus(n3,succ(succ(X))),plus(succ(X),n4)) )],[refute_2_51,refute_2_52]) ).
cnf(refute_2_54,plain,
plus(n3,succ(succ(X))) = plus(n4,succ(X)),
inference(resolve,[$cnf( $equal(plus(succ(X),n4),plus(n4,succ(X))) )],[refute_2_50,refute_2_53]) ).
cnf(refute_2_55,plain,
plus(succ(succ(X)),n3) = plus(n3,succ(succ(X))),
inference(subst,[],[refute_2_26:[bind(X,$fot(succ(succ(X))))]]) ).
cnf(refute_2_56,plain,
( plus(n3,succ(succ(X))) != plus(n4,succ(X))
| plus(succ(succ(X)),n3) != plus(n3,succ(succ(X)))
| plus(succ(succ(X)),n3) = plus(n4,succ(X)) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(succ(succ(X)),n3))),bind(Y0,$fot(plus(n3,succ(succ(X))))),bind(Z,$fot(plus(n4,succ(X))))]]) ).
cnf(refute_2_57,plain,
( plus(n3,succ(succ(X))) != plus(n4,succ(X))
| plus(succ(succ(X)),n3) = plus(n4,succ(X)) ),
inference(resolve,[$cnf( $equal(plus(succ(succ(X)),n3),plus(n3,succ(succ(X)))) )],[refute_2_55,refute_2_56]) ).
cnf(refute_2_58,plain,
plus(succ(succ(X)),n3) = plus(n4,succ(X)),
inference(resolve,[$cnf( $equal(plus(n3,succ(succ(X))),plus(n4,succ(X))) )],[refute_2_54,refute_2_57]) ).
cnf(refute_2_59,plain,
succ(succ(succ(succ(succ(X))))) = plus(succ(succ(X)),n3),
inference(subst,[],[refute_2_21:[bind(X,$fot(succ(succ(X))))]]) ).
cnf(refute_2_60,plain,
( plus(succ(succ(X)),n3) != plus(n4,succ(X))
| succ(succ(succ(succ(succ(X))))) != plus(succ(succ(X)),n3)
| succ(succ(succ(succ(succ(X))))) = plus(n4,succ(X)) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(succ(succ(succ(succ(succ(X))))))),bind(Y0,$fot(plus(succ(succ(X)),n3))),bind(Z,$fot(plus(n4,succ(X))))]]) ).
cnf(refute_2_61,plain,
( plus(succ(succ(X)),n3) != plus(n4,succ(X))
| succ(succ(succ(succ(succ(X))))) = plus(n4,succ(X)) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(succ(X))))),plus(succ(succ(X)),n3)) )],[refute_2_59,refute_2_60]) ).
cnf(refute_2_62,plain,
succ(succ(succ(succ(succ(X))))) = plus(n4,succ(X)),
inference(resolve,[$cnf( $equal(plus(succ(succ(X)),n3),plus(n4,succ(X))) )],[refute_2_58,refute_2_61]) ).
cnf(refute_2_63,plain,
( plus(X,n5) != succ(succ(succ(succ(succ(X)))))
| succ(succ(succ(succ(succ(X))))) != plus(n4,succ(X))
| plus(X,n5) = plus(n4,succ(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(X,n5),plus(n4,succ(X))) ),[0],$fot(succ(succ(succ(succ(succ(X))))))]]) ).
cnf(refute_2_64,plain,
( plus(X,n5) != succ(succ(succ(succ(succ(X)))))
| plus(X,n5) = plus(n4,succ(X)) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(succ(X))))),plus(n4,succ(X))) )],[refute_2_62,refute_2_63]) ).
cnf(refute_2_65,plain,
plus(X,n5) = plus(n4,succ(X)),
inference(resolve,[$cnf( $equal(plus(X,n5),succ(succ(succ(succ(succ(X)))))) )],[refute_2_12,refute_2_64]) ).
cnf(refute_2_66,plain,
plus(n0,n5) = plus(n4,succ(n0)),
inference(subst,[],[refute_2_65:[bind(X,$fot(n0))]]) ).
cnf(refute_2_67,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_2_19]) ).
cnf(refute_2_68,plain,
( plus(n0,n5) != plus(n4,succ(n0))
| succ(n0) != n1
| plus(n0,n5) = plus(n4,n1) ),
introduced(tautology,[equality,[$cnf( $equal(plus(n0,n5),plus(n4,succ(n0))) ),[1,1],$fot(n1)]]) ).
cnf(refute_2_69,plain,
( plus(n0,n5) != plus(n4,succ(n0))
| plus(n0,n5) = plus(n4,n1) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_2_67,refute_2_68]) ).
cnf(refute_2_70,plain,
plus(n0,n5) = plus(n4,n1),
inference(resolve,[$cnf( $equal(plus(n0,n5),plus(n4,succ(n0))) )],[refute_2_66,refute_2_69]) ).
cnf(refute_2_71,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(canonicalize,[],[normalize_2_20]) ).
cnf(refute_2_72,plain,
( plus(X,n5) != plus(n4,succ(X))
| plus(n4,succ(X)) = plus(X,n5) ),
inference(subst,[],[refute_2_19:[bind(X0,$fot(plus(X,n5))),bind(Y0,$fot(plus(n4,succ(X))))]]) ).
cnf(refute_2_73,plain,
plus(n4,succ(X)) = plus(X,n5),
inference(resolve,[$cnf( $equal(plus(X,n5),plus(n4,succ(X))) )],[refute_2_65,refute_2_72]) ).
cnf(refute_2_74,plain,
plus(n4,succ(n0)) = plus(n0,n5),
inference(subst,[],[refute_2_73:[bind(X,$fot(n0))]]) ).
cnf(refute_2_75,plain,
plus(succ(n0),n4) = plus(n4,succ(n0)),
inference(subst,[],[refute_2_49:[bind(X,$fot(succ(n0)))]]) ).
cnf(refute_2_76,plain,
( plus(n4,succ(n0)) != plus(n0,n5)
| plus(succ(n0),n4) != plus(n4,succ(n0))
| plus(succ(n0),n4) = plus(n0,n5) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(succ(n0),n4))),bind(Y0,$fot(plus(n4,succ(n0)))),bind(Z,$fot(plus(n0,n5)))]]) ).
cnf(refute_2_77,plain,
( plus(n4,succ(n0)) != plus(n0,n5)
| plus(succ(n0),n4) = plus(n0,n5) ),
inference(resolve,[$cnf( $equal(plus(succ(n0),n4),plus(n4,succ(n0))) )],[refute_2_75,refute_2_76]) ).
cnf(refute_2_78,plain,
plus(succ(n0),n4) = plus(n0,n5),
inference(resolve,[$cnf( $equal(plus(n4,succ(n0)),plus(n0,n5)) )],[refute_2_74,refute_2_77]) ).
cnf(refute_2_79,plain,
plus(n3,succ(succ(n0))) = plus(succ(n0),n4),
inference(subst,[],[refute_2_38:[bind(X,$fot(succ(n0)))]]) ).
cnf(refute_2_80,plain,
( plus(n3,succ(succ(n0))) != plus(succ(n0),n4)
| plus(succ(n0),n4) != plus(n0,n5)
| plus(n3,succ(succ(n0))) = plus(n0,n5) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(n3,succ(succ(n0))))),bind(Y0,$fot(plus(succ(n0),n4))),bind(Z,$fot(plus(n0,n5)))]]) ).
cnf(refute_2_81,plain,
( plus(succ(n0),n4) != plus(n0,n5)
| plus(n3,succ(succ(n0))) = plus(n0,n5) ),
inference(resolve,[$cnf( $equal(plus(n3,succ(succ(n0))),plus(succ(n0),n4)) )],[refute_2_79,refute_2_80]) ).
cnf(refute_2_82,plain,
plus(n3,succ(succ(n0))) = plus(n0,n5),
inference(resolve,[$cnf( $equal(plus(succ(n0),n4),plus(n0,n5)) )],[refute_2_78,refute_2_81]) ).
cnf(refute_2_83,plain,
plus(succ(succ(n0)),n3) = plus(n3,succ(succ(n0))),
inference(subst,[],[refute_2_26:[bind(X,$fot(succ(succ(n0))))]]) ).
cnf(refute_2_84,plain,
( plus(n3,succ(succ(n0))) != plus(n0,n5)
| plus(succ(succ(n0)),n3) != plus(n3,succ(succ(n0)))
| plus(succ(succ(n0)),n3) = plus(n0,n5) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(succ(succ(n0)),n3))),bind(Y0,$fot(plus(n3,succ(succ(n0))))),bind(Z,$fot(plus(n0,n5)))]]) ).
cnf(refute_2_85,plain,
( plus(n3,succ(succ(n0))) != plus(n0,n5)
| plus(succ(succ(n0)),n3) = plus(n0,n5) ),
inference(resolve,[$cnf( $equal(plus(succ(succ(n0)),n3),plus(n3,succ(succ(n0)))) )],[refute_2_83,refute_2_84]) ).
cnf(refute_2_86,plain,
plus(succ(succ(n0)),n3) = plus(n0,n5),
inference(resolve,[$cnf( $equal(plus(n3,succ(succ(n0))),plus(n0,n5)) )],[refute_2_82,refute_2_85]) ).
cnf(refute_2_87,plain,
succ(succ(succ(succ(succ(n0))))) = plus(succ(succ(n0)),n3),
inference(subst,[],[refute_2_21:[bind(X,$fot(succ(succ(n0))))]]) ).
cnf(refute_2_88,plain,
( plus(succ(succ(n0)),n3) != plus(n0,n5)
| succ(succ(succ(succ(succ(n0))))) != plus(succ(succ(n0)),n3)
| succ(succ(succ(succ(succ(n0))))) = plus(n0,n5) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(succ(succ(succ(succ(succ(n0))))))),bind(Y0,$fot(plus(succ(succ(n0)),n3))),bind(Z,$fot(plus(n0,n5)))]]) ).
cnf(refute_2_89,plain,
( plus(succ(succ(n0)),n3) != plus(n0,n5)
| succ(succ(succ(succ(succ(n0))))) = plus(n0,n5) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(succ(n0))))),plus(succ(succ(n0)),n3)) )],[refute_2_87,refute_2_88]) ).
cnf(refute_2_90,plain,
succ(succ(succ(succ(succ(n0))))) = plus(n0,n5),
inference(resolve,[$cnf( $equal(plus(succ(succ(n0)),n3),plus(n0,n5)) )],[refute_2_86,refute_2_89]) ).
cnf(refute_2_91,plain,
( succ(succ(succ(succ(succ(n0))))) != n5
| succ(succ(succ(succ(succ(n0))))) != plus(n0,n5)
| plus(n0,n5) = n5 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(succ(succ(succ(n0))))),n5) ),[0],$fot(plus(n0,n5))]]) ).
cnf(refute_2_92,plain,
( succ(succ(succ(succ(succ(n0))))) != n5
| plus(n0,n5) = n5 ),
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(succ(n0))))),plus(n0,n5)) )],[refute_2_90,refute_2_91]) ).
cnf(refute_2_93,plain,
plus(n0,n5) = n5,
inference(resolve,[$cnf( $equal(succ(succ(succ(succ(succ(n0))))),n5) )],[refute_2_71,refute_2_92]) ).
cnf(refute_2_94,plain,
( plus(n0,n5) != n5
| plus(n0,n5) != plus(n4,n1)
| n5 = plus(n4,n1) ),
introduced(tautology,[equality,[$cnf( $equal(plus(n0,n5),plus(n4,n1)) ),[0],$fot(n5)]]) ).
cnf(refute_2_95,plain,
( plus(n0,n5) != plus(n4,n1)
| n5 = plus(n4,n1) ),
inference(resolve,[$cnf( $equal(plus(n0,n5),n5) )],[refute_2_93,refute_2_94]) ).
cnf(refute_2_96,plain,
plus(n1,X) = succ(X),
inference(canonicalize,[],[normalize_2_22]) ).
cnf(refute_2_97,plain,
plus(n1,n4) = succ(n4),
inference(subst,[],[refute_2_96:[bind(X,$fot(n4))]]) ).
cnf(refute_2_98,plain,
plus(n4,n1) = plus(n1,n4),
inference(subst,[],[refute_2_47:[bind(X,$fot(n1))]]) ).
cnf(refute_2_99,plain,
( plus(n1,n4) != succ(n4)
| plus(n4,n1) != plus(n1,n4)
| plus(n4,n1) = succ(n4) ),
inference(subst,[],[refute_2_30:[bind(X0,$fot(plus(n4,n1))),bind(Y0,$fot(plus(n1,n4))),bind(Z,$fot(succ(n4)))]]) ).
cnf(refute_2_100,plain,
( plus(n1,n4) != succ(n4)
| plus(n4,n1) = succ(n4) ),
inference(resolve,[$cnf( $equal(plus(n4,n1),plus(n1,n4)) )],[refute_2_98,refute_2_99]) ).
cnf(refute_2_101,plain,
plus(n4,n1) = succ(n4),
inference(resolve,[$cnf( $equal(plus(n1,n4),succ(n4)) )],[refute_2_97,refute_2_100]) ).
cnf(refute_2_102,plain,
( n5 != plus(n4,n1)
| plus(n4,n1) != succ(n4)
| n5 = succ(n4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(n5,succ(n4)) ),[0],$fot(plus(n4,n1))]]) ).
cnf(refute_2_103,plain,
( n5 != plus(n4,n1)
| n5 = succ(n4) ),
inference(resolve,[$cnf( $equal(plus(n4,n1),succ(n4)) )],[refute_2_101,refute_2_102]) ).
cnf(refute_2_104,plain,
( plus(n0,n5) != plus(n4,n1)
| n5 = succ(n4) ),
inference(resolve,[$cnf( $equal(n5,plus(n4,n1)) )],[refute_2_95,refute_2_103]) ).
cnf(refute_2_105,plain,
n5 = succ(n4),
inference(resolve,[$cnf( $equal(plus(n0,n5),plus(n4,n1)) )],[refute_2_70,refute_2_104]) ).
cnf(refute_2_106,plain,
( n5 != succ(n4)
| succ(n4) = n5 ),
inference(subst,[],[refute_2_19:[bind(X0,$fot(n5)),bind(Y0,$fot(succ(n4)))]]) ).
cnf(refute_2_107,plain,
succ(n4) = n5,
inference(resolve,[$cnf( $equal(n5,succ(n4)) )],[refute_2_105,refute_2_106]) ).
cnf(refute_2_108,plain,
( pred(succ(n4)) != n4
| succ(n4) != n5
| pred(n5) = n4 ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(n4)),n4) ),[0,0],$fot(n5)]]) ).
cnf(refute_2_109,plain,
( pred(succ(n4)) != n4
| pred(n5) = n4 ),
inference(resolve,[$cnf( $equal(succ(n4),n5) )],[refute_2_107,refute_2_108]) ).
cnf(refute_2_110,plain,
pred(n5) = n4,
inference(resolve,[$cnf( $equal(pred(succ(n4)),n4) )],[refute_2_11,refute_2_109]) ).
cnf(refute_2_111,plain,
( pred(n5) != n4
| ~ leq(n0,n4)
| leq(n0,pred(n5)) ),
introduced(tautology,[equality,[$cnf( ~ leq(n0,pred(n5)) ),[1],$fot(n4)]]) ).
cnf(refute_2_112,plain,
( ~ leq(n0,n4)
| leq(n0,pred(n5)) ),
inference(resolve,[$cnf( $equal(pred(n5),n4) )],[refute_2_110,refute_2_111]) ).
cnf(refute_2_113,plain,
~ leq(n0,n4),
inference(resolve,[$cnf( leq(n0,pred(n5)) )],[refute_2_112,refute_2_9]) ).
cnf(refute_2_114,plain,
$false,
inference(resolve,[$cnf( leq(n0,n4) )],[refute_2_3,refute_2_113]) ).
fof(negate_3_0,plain,
~ ( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1))
& leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1)) )
=> leq(pv10,minus(n135300,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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV069+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 19:46:37 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.04/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.04/1.22
% 1.04/1.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.07/1.23
%------------------------------------------------------------------------------